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Tesser L, Splettstoesser J. Out-of-Equilibrium Fluctuation-Dissipation Bounds. PHYSICAL REVIEW LETTERS 2024; 132:186304. [PMID: 38759166 DOI: 10.1103/physrevlett.132.186304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Accepted: 04/02/2024] [Indexed: 05/19/2024]
Abstract
We prove a general inequality between the charge current and its fluctuations valid for any weakly interacting coherent electronic conductor and for any stationary out-of-equilibrium condition, thereby going beyond established fluctuation-dissipation relations. The developed fluctuation-dissipation bound saturates at large temperature bias and reveals additional insight for heat engines, since it limits the output power by power fluctuations. It is valid when the thermodynamic uncertainty relations break down due to quantum effects and provides stronger constraints close to thermovoltage.
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Affiliation(s)
- Ludovico Tesser
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, S-412 96 Göteborg, Sweden
| | - Janine Splettstoesser
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, S-412 96 Göteborg, Sweden
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2
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Aslyamov T, Esposito M. Nonequilibrium Response for Markov Jump Processes: Exact Results and Tight Bounds. PHYSICAL REVIEW LETTERS 2024; 132:037101. [PMID: 38307069 DOI: 10.1103/physrevlett.132.037101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2023] [Revised: 10/13/2023] [Accepted: 12/14/2023] [Indexed: 02/04/2024]
Abstract
Generalizing response theory of open systems far from equilibrium is a central quest of nonequilibrium statistical physics. Using stochastic thermodynamics, we develop an algebraic method to study the static response of nonequilibrium steady state to arbitrary perturbations. This allows us to derive explicit expressions for the response of edge currents as well as traffic to perturbations in kinetic barriers and driving forces. We also show that these responses satisfy very simple bounds. For the response to energy perturbations, we straightforwardly recover results obtained using nontrivial graph-theoretical methods.
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Affiliation(s)
- Timur Aslyamov
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Massimiliano Esposito
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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3
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Fernandes Martins G, Horowitz JM. Topologically constrained fluctuations and thermodynamics regulate nonequilibrium response. Phys Rev E 2023; 108:044113. [PMID: 37978593 DOI: 10.1103/physreve.108.044113] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Accepted: 08/07/2023] [Indexed: 11/19/2023]
Abstract
The limits on a system's response to external perturbations inform our understanding of how physical properties can be shaped by microscopic characteristics. Here, we derive constraints on the steady-state nonequilibrium response of physical observables in terms of the topology of the microscopic state space and the strength of thermodynamic driving. Notably, evaluation of these limits requires no kinetic information beyond the state-space structure. When applied to models of receptor binding, we find that sensitivity is bounded by the steepness of a Hill function with a Hill coefficient enhanced by the chemical driving beyond the structural equilibrium limit.
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Affiliation(s)
| | - Jordan M Horowitz
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48104, USA
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4
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Kasuga K, Yoshimori A. Nonintegral form of the reciprocal relation associated with violation of the fluctuation response relation. Phys Rev E 2023; 108:034109. [PMID: 37849163 DOI: 10.1103/physreve.108.034109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2022] [Accepted: 08/15/2023] [Indexed: 10/19/2023]
Abstract
We extend Onsager's reciprocal relation to systems in a nonequilibrium steady state. While Onsager's reciprocal relation concerns the kinetic (Onsager) coefficient, the extended reciprocal relation concerns violation of the fluctuation response relation (FRR) for mechanical and thermal perturbations. This extended relation holds at each frequency when the extent of the FRR violation is expressed in a frequency domain. This nonintegral form distinguishes the extended relation from previous relations expressed by integration over a frequency. To obtain this relation, we consider one-particle one-dimensional systems described by an overdamped Langevin equation with a force driving the system away from equilibrium. We assume a special property of the potential in the system. From this Langevin equation, we obtain the Fokker-Planck (FP) equation describing the time evolution of the distribution function of the particle. Using the FP equation, we calculate the responses of the particle velocity and heat current by applying time-dependent perturbations of the driving force and temperature. We express the extent of the FRR violation in terms of these responses with time correlation functions and expand them in powers of the FP operator. This reciprocal relation is valid far from equilibrium. One can also confirm this reciprocal relation through experiments with systems such as colloidal suspensions because the FRR violation can be experimentally observed.
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Affiliation(s)
- Kotaro Kasuga
- Department of Physics, Niigata University, Niigata 950-2181, Japan
| | - Akira Yoshimori
- Department of Physics, Niigata University, Niigata 950-2181, Japan
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5
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Pérez-Cervera A, Gutkin B, Thomas PJ, Lindner B. A universal description of stochastic oscillators. Proc Natl Acad Sci U S A 2023; 120:e2303222120. [PMID: 37432992 PMCID: PMC10629544 DOI: 10.1073/pnas.2303222120] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 05/18/2023] [Indexed: 07/13/2023] Open
Abstract
Many systems in physics, chemistry, and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example, linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. Here, we introduce a nonlinear transformation of stochastic oscillators to a complex-valued function [Formula: see text](x) that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. The function [Formula: see text] (x) is the eigenfunction of the Kolmogorov backward operator with the least negative (but nonvanishing) eigenvalue λ1 = μ1 + iω1. The resulting power spectrum of the complex-valued function is exactly given by a Lorentz spectrum with peak frequency ω1 and half-width μ1; its susceptibility with respect to a weak external forcing is given by a simple one-pole filter, centered around ω1; and the cross-spectrum between two coupled oscillators can be easily expressed by a combination of the spontaneous power spectra of the uncoupled systems and their susceptibilities. Our approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators.
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Affiliation(s)
- Alberto Pérez-Cervera
- Department of Applied Mathematics, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Madrid28040, Spain
| | - Boris Gutkin
- Group for Neural Theory, LNC2 INSERM U960, Département d’Etudes Cognitives, Ecole Normale Supérieure - Paris Science Letters University, Paris75005, France
| | - Peter J. Thomas
- Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, Cleveland, OH44106
| | - Benjamin Lindner
- Bernstein Center for Computational Neuroscience Berlin, Berlin10115, Germany
- Department of Physics, Humboldt Universität zu Berlin, BerlinD-12489, Germany
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6
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Minoguchi M, Sasa SI. Divergent Stiffness of One-Dimensional Growing Interfaces. PHYSICAL REVIEW LETTERS 2023; 130:197101. [PMID: 37243631 DOI: 10.1103/physrevlett.130.197101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 01/12/2023] [Accepted: 04/13/2023] [Indexed: 05/29/2023]
Abstract
When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the stiffness exhibits divergent behavior in the large system size limit for a growing interface with thermal noise, which has never been observed for equilibrium interfaces. Furthermore, by connecting the effective surface tension with a space-time correlation function, we elucidate the mechanism that anomalous dynamical fluctuations lead to divergent stiffness.
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Affiliation(s)
| | - Shin-Ichi Sasa
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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7
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Chun HM, Horowitz JM. Trade-offs between number fluctuations and response in nonequilibrium chemical reaction networks. J Chem Phys 2023; 158:2888610. [PMID: 37144710 DOI: 10.1063/5.0148662] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 04/17/2023] [Indexed: 05/06/2023] Open
Abstract
We study the response of chemical reaction networks driven far from equilibrium to logarithmic perturbations of reaction rates. The response of the mean number of a chemical species is observed to be quantitively limited by number fluctuations and the maximum thermodynamic driving force. We prove these trade-offs for linear chemical reaction networks and a class of nonlinear chemical reaction networks with a single chemical species. Numerical results for several model systems support the conclusion that these trade-offs continue to hold for a broad class of chemical reaction networks, though their precise form appears to sensitively depend on the deficiency of the network.
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Affiliation(s)
- Hyun-Myung Chun
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, South Korea
| | - Jordan M Horowitz
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48104, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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8
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Dadhichi LP, Kroy K. Time-reversal symmetries and equilibriumlike Langevin equations. Phys Rev E 2023; 107:044106. [PMID: 37198792 DOI: 10.1103/physreve.107.044106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Accepted: 03/20/2023] [Indexed: 05/19/2023]
Abstract
Graham has shown [Z. Phys. B 26, 397 (1977)0340-224X10.1007/BF01570750] that a fluctuation-dissipation relation can be imposed on a class of nonequilibrium Markovian Langevin equations that admit a stationary solution of the corresponding Fokker-Planck equation. The resulting equilibrium form of the Langevin equation is associated with a nonequilibrium Hamiltonian. Here we provide some explicit insight into how this Hamiltonian may lose its time-reversal invariance and how the "reactive" and "dissipative" fluxes loose their distinct time-reversal symmetries. The antisymmetric coupling matrix between forces and fluxes no longer originates from Poisson brackets and the "reactive" fluxes contribute to the ("housekeeping") entropy production, in the steady state. The time-reversal even and odd parts of the nonequilibrium Hamiltonian contribute in qualitatively different but physically instructive ways to the entropy. We find instances where fluctuations due to noise are solely responsible for the dissipation. Finally, this structure gives rise to a new, physically pertinent instance of frenesy.
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Affiliation(s)
| | - Klaus Kroy
- Institute for Theoretical Physics, Leipzig University, 04103 Leipzig, Germany
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9
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Woodcox M, Mahata A, Hagerstrom A, Stelson A, Muzny C, Sundararaman R, Schwarz K. Simulating dielectric spectra: A demonstration of the direct electric field method and a new model for the nonlinear dielectric response. J Chem Phys 2023; 158:124122. [PMID: 37003751 DOI: 10.1063/5.0143425] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023] Open
Abstract
We demonstrate a method to compute the dielectric spectra of fluids in molecular dynamics (MD) by directly applying electric fields to the simulation. We obtain spectra from MD simulations with low magnitude electric fields (≈0.01 V/Å) in agreement with spectra from the fluctuation-dissipation method for water and acetonitrile. We examine this method's trade-off between noise at low field magnitudes and the nonlinearity of the response at higher field magnitudes. We then apply the Booth equation to describe the nonlinear response of both fluids at low frequency (0.1 GHz) and high field magnitude (up to 0.5 V/Å). We develop a model of the frequency-dependent nonlinear response by combining the Booth description of the static nonlinear dielectric response of fluids with the frequency-dependent linear dielectric response of the Debye model. We find good agreement between our model and the MD simulations of the nonlinear dielectric response for both acetonitrile and water.
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Affiliation(s)
- Michael Woodcox
- Theiss Research, P. O. Box 127, La Jolla, California 92038, USA
| | - Avik Mahata
- Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Dr., Gaithersburg, Maryland 20899, USA
| | - Aaron Hagerstrom
- Communications Technology Laboratory, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - Angela Stelson
- Communications Technology Laboratory, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - Chris Muzny
- Material Measurement Laboratory, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - Ravishankar Sundararaman
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, 110 8th St., Troy, New York 12180, USA
| | - Kathleen Schwarz
- Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Dr., Gaithersburg, Maryland 20899, USA
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10
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Sokolov IM. Linear Response and Fluctuation-Dissipation Relations for Brownian Motion under Resetting. PHYSICAL REVIEW LETTERS 2023; 130:067101. [PMID: 36827569 DOI: 10.1103/physrevlett.130.067101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Accepted: 01/17/2023] [Indexed: 06/18/2023]
Abstract
We consider fluctuation-dissipation relations (FDRs) for a Brownian motion under renewal resetting with arbitrary waiting time distribution between the resetting events. We show that if the distribution of waiting times of the resetting process possesses the second moment, the usual (generalized) FDR and the equivalent generalized Einstein's relation (GER) apply for the response function of the coordinate. If the second moment of waiting times diverges but the first one stays finite, the static susceptibility diverges, the usual FDR breaks down, but the GER still applies. In any of these situations, the fluctuation dissipation relations define the effective temperature of the system which is twice as high as the temperature of the medium in which the Brownian motion takes place.
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Affiliation(s)
- Igor M Sokolov
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany and IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, D-12489 Berlin, Germany
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11
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Yang YJ, Qian H. Time-translational symmetry in statistical dynamics dictates Einstein relation, Green-Kubo formula, and their generalizations. Phys Rev E 2023; 107:024110. [PMID: 36932497 DOI: 10.1103/physreve.107.024110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Accepted: 01/23/2023] [Indexed: 02/11/2023]
Abstract
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent, components contributing to the overall fluctuations of the dynamics, representing the uncertainties in the past and in the future. We show that fluctuation-dissipation relations of the two aforementioned components, such as the Einstein relation and the Green-Kubo formula, can be formulated for any stochastic process with a steady state, without additional supposition of the process being Markovian, reversible, or linear. Further, by considering the adjoint process defined by the time reversal at the steady state, we show that reversibility in equilibrium leads to an additional symmetry in the covariance between system's state and drift. Potential directions of further generalizing our results to processes without steady states is briefly discussed.
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Affiliation(s)
- Ying-Jen Yang
- Laufer Center for Physical and Quantitative Biology, State University of New York, Stony Brook, New York 11794, USA
| | - Hong Qian
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA
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12
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Öztürk FE, Vewinger F, Weitz M, Schmitt J. Fluctuation-Dissipation Relation for a Bose-Einstein Condensate of Photons. PHYSICAL REVIEW LETTERS 2023; 130:033602. [PMID: 36763390 DOI: 10.1103/physrevlett.130.033602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Revised: 07/28/2022] [Accepted: 12/22/2022] [Indexed: 06/18/2023]
Abstract
For equilibrium systems, the magnitude of thermal fluctuations is closely linked to the dissipative response to external perturbations. This fluctuation-dissipation relation has been described for material particles in a wide range of fields. Here, we experimentally probe the relation between the number fluctuations and the response function for a Bose-Einstein condensate of photons coupled to a dye reservoir, demonstrating the fluctuation-dissipation relation for a quantum gas of light. The observed agreement of the scale factor with the environment temperature both directly confirms the thermal nature of the optical condensate and demonstrates the validity of the fluctuation-dissipation theorem for a Bose-Einstein condensate.
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Affiliation(s)
- Fahri Emre Öztürk
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Frank Vewinger
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Martin Weitz
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Julian Schmitt
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
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13
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Lindner B. Fluctuation-Dissipation Relations for Spiking Neurons. PHYSICAL REVIEW LETTERS 2022; 129:198101. [PMID: 36399734 DOI: 10.1103/physrevlett.129.198101] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Revised: 09/27/2022] [Accepted: 10/17/2022] [Indexed: 06/16/2023]
Abstract
Spontaneous fluctuations and stimulus response are essential features of neural functioning, but how they are connected is poorly understood. I derive fluctuation-dissipation relations (FDR) between the spontaneous spike and voltage correlations and the firing rate susceptibility for (i) the leaky integrate-and-fire (IF) model with white noise and (ii) an IF model with arbitrary voltage dependence, an adaptation current, and correlated noise. The FDRs can be used to derive thus far unknown statistics analytically [model (i)] or the otherwise inaccessible intrinsic noise statistics [model (ii)].
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Affiliation(s)
- Benjamin Lindner
- Bernstein Center for Computational Neuroscience Berlin, Philippstraße 13, Haus 2, 10115 Berlin, Germany and Physics Department of Humboldt University Berlin, Newtonstraße 15, 12489 Berlin, Germany
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14
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Ghosal A, Bisker G. Inferring entropy production rate from partially observed Langevin dynamics under coarse-graining. Phys Chem Chem Phys 2022; 24:24021-24031. [PMID: 36065766 PMCID: PMC7613705 DOI: 10.1039/d2cp03064k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The entropy production rate (EPR) measures time-irreversibility in systems operating far from equilibrium. The challenge in estimating the EPR for a continuous variable system is the finite spatiotemporal resolution and the limited accessibility to all of the nonequilibrium degrees of freedom. Here, we estimate the irreversibility in partially observed systems following oscillatory dynamics governed by coupled overdamped Langevin equations. We coarse-grain an observed variable of a nonequilibrium driven system into a few discrete states and estimate a lower bound on the total EPR. As a model system, we use hair-cell bundle oscillations driven by molecular motors, such that the bundle tip position is observed, but the positions of the motors are hidden. In the observed variable space, the underlying driven process exhibits second-order semi-Markov statistics. The waiting time distributions (WTD), associated with transitions among the coarse-grained states, are non-exponential and convey the information on the broken time-reversal symmetry. By invoking the underlying time-irreversibility, we calculate a lower bound on the total EPR from the Kullback-Leibler divergence (KLD) between WTD. We show that the mean dwell-time asymmetry factor - the ratio between the mean dwell-times along the forward direction and the backward direction, can qualitatively measure the degree of broken time reversal symmetry and increases with finer spatial resolution. Finally, we apply our methodology to a continuous-time discrete Markov chain model, coarse-grained into a linear system exhibiting second-order semi-Markovian statistics, and demonstrate the estimation of a lower bound on the total EPR from irreversibility manifested only in the WTD.
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Affiliation(s)
- Aishani Ghosal
- Department of Biomedical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel.
| | - Gili Bisker
- Department of Biomedical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel. .,Center for Physics and Chemistry of Living Systems, Tel-Aviv University, Tel Aviv 6997801, Israel.,Center for Nanoscience and Nanotechnology, Tel-Aviv University, Tel Aviv 6997801, Israel.,Center for Light-Matter Interaction, Tel-Aviv University, Tel Aviv 6997801, Israel
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15
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Shiraishi N. Time-Symmetric Current and Its Fluctuation Response Relation around Nonequilibrium Stalling Stationary State. PHYSICAL REVIEW LETTERS 2022; 129:020602. [PMID: 35867465 DOI: 10.1103/physrevlett.129.020602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Revised: 04/15/2022] [Accepted: 06/13/2022] [Indexed: 06/15/2023]
Abstract
We propose a time-symmetric counterpart of the current in stochastic thermodynamics named the time-symmetric current. This quantity is defined with empirical measures and thus is symmetric under time reversal, while its ensemble average reproduces the amount of the average current. We prove that this time-symmetric current satisfies the fluctuation-response relation in the conventional form but with sign inversion. Remarkably, this fluctuation-response relation holds not only around equilibrium states but also around nonequilibrium stationary states if observed currents stall. The obtained relation also serves as an experimental tool for probing the value of a bare transition rate by measuring only time-integrated empirical measures.
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Affiliation(s)
- Naoto Shiraishi
- Department of Physics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan
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16
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How a Nonequilibrium Bath and a Potential Well Lead to Broken Time-Reversal Symmetry—First-Order Corrections on Fluctuation–Dissipation Relations. Symmetry (Basel) 2022. [DOI: 10.3390/sym14051042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
The noise that is associated with nonequilibrium processes commonly features more outliers and is therefore often taken to be Lévy noise. For a Langevin particle that is subjected to Lévy noise, the kicksizes are drawn not from a Gaussian distribution, but from an α-stable distribution. For a Gaussian-noise-subjected particle in a potential well, microscopic reversibility applies. However, it appears that the time-reversal-symmetry is broken for a Lévy-noise-subjected particle in a potential well. Major obstacles in the analysis of Langevin equations with Lévy noise are the lack of simple analytic formulae and the infinite variance of the α-stable distribution. We propose a measure for the violation of time-reversal symmetry, and we present a procedure in which this measure is central to a controlled imposing of time-reversal asymmetry. The procedure leads to behavior that mimics much of the effects of Lévy noise. Our imposing of such nonequilibrium leads to concise analytic formulae and does not yield any divergent variances. Most importantly, the theory leads to simple corrections on the Fluctuation–Dissipation Relation.
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17
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Chen S, Pirhadi E, Yong X. Viscoelastic necking dynamics between attractive microgels. J Colloid Interface Sci 2022; 618:283-289. [PMID: 35344881 DOI: 10.1016/j.jcis.2022.03.048] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Revised: 03/10/2022] [Accepted: 03/11/2022] [Indexed: 12/01/2022]
Abstract
HYPOTHESIS Microgels can deform and interpenetrate and display colloid/polymer duality. The effective interaction of microgels in the collapsed state is governed by the interplay of polymer-solvent interfacial tension and bulk elasticity. A connecting neck is shown to mediate microgel interaction, but its temporal evolution has not been addressed. We hypothesize that the necking dynamics of attractive microgels exhibits liquid-like or solid-like behavior over different time and length scales. EXPERIMENTS We simulate the merging and pinching of attractive microgels with different crosslinking densities in explicit solvent using dissipative particle dynamics. The temporal coalescence dynamics of microgels is investigated and compared with simple liquid and polymeric droplets. We model the neck growth on long time scales using Maxwell model of polymer relaxation and compare the theoretical prediction with simulation data. The mechanical strength of the neck is characterized systematically via simulated pinch-off of microgels by steered molecular dynamics. FINDINGS We evidence a crossover in the coalescence dynamics reflecting the viscoelastic signature of microgels. In contrast to the common knowledge that viscoelastic materials respond elastically on short time scales, the early expansion of the microgel neck exhibits a linear behavior, similar to the viscous coalescence of liquid droplets. However, the late regime with arrested dynamics resembles sintering of solid particles. Through an analytical model relating microgel dynamics to neck growth, we show that the long-term behavior is governed by stress relaxation of the polymers in the neck region and predict an exponential decay in the rate of growth, which agrees favorably with the simulation. Different from coalescence, the thread thinning in microgel breakup primarily highlights its polymeric characteristics.
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Affiliation(s)
- Shensheng Chen
- Department of Mechanical Engineering, Binghamton University, The State University of New York, Binghamton, NY 13902, USA
| | - Emad Pirhadi
- Department of Mechanical Engineering, Binghamton University, The State University of New York, Binghamton, NY 13902, USA
| | - Xin Yong
- Department of Mechanical Engineering, Binghamton University, The State University of New York, Binghamton, NY 13902, USA.
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18
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Liu K, Qin H, Tian M, Zhang L, Mi J. Towards a comprehensive optimization of dielectric and viscoelastic performance of poly(ethylene-co-methyl acrylate) through chain sequence regulation. POLYMER 2022. [DOI: 10.1016/j.polymer.2022.124657] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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19
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Gao Q, Chun HM, Horowitz JM. Thermodynamic constraints on the nonequilibrium response of one-dimensional diffusions. Phys Rev E 2022; 105:L012102. [PMID: 35193184 DOI: 10.1103/physreve.105.l012102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 12/21/2021] [Indexed: 11/07/2022]
Abstract
We analyze the static response to perturbations of nonequilibrium steady states that can be modeled as one-dimensional diffusions on the circle. We demonstrate that an arbitrary perturbation can be broken up into a combination of three specific classes of perturbations that can be fruitfully addressed individually. For each class, we derive a simple formula that quantitatively characterizes the response in terms of the strength of nonequilibrium driving valid arbitrarily far from equilibrium.
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Affiliation(s)
- Qi Gao
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Hyun-Myung Chun
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Jordan M Horowitz
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.,Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA.,Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48104, USA
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20
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Dodin A, Willard AP. Nonequilibrium Work Relations and Response Theories in Ensemble Quantum Systems. J Phys Chem Lett 2021; 12:11151-11157. [PMID: 34757738 DOI: 10.1021/acs.jpclett.1c01315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We develop a nonequilibrium response theory for macroscopic quantum systems that separates the contributions of ensemble heterogeneity and intrinsic quantum uncertainty. To accomplish this, we describe systems with a quantum P-ensemble, which goes beyond the standard density matrix description by explicitly specifying the classical heterogeneity between individual quantum systems in an ensemble. We use the P-ensemble formalism to present quantum generalizations of linear response theory and the Jarzynski nonequilibrium work relation. We derive these generalizations from a Bochkov-Kuzovlev generating functional for quantum P-ensembles, which can be further utilized to derive all orders of response theory that apply to ensemble quantum systems. We contrast these developments with their ρ-ensemble analogs, and we discuss how these P-ensemble theories provide a guide for an effective application of single molecule experiments.
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Affiliation(s)
- Amro Dodin
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Adam P Willard
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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21
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Marguet B, Agoritsas E, Canet L, Lecomte V. Supersymmetries in nonequilibrium Langevin dynamics. Phys Rev E 2021; 104:044120. [PMID: 34781484 DOI: 10.1103/physreve.104.044120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 10/01/2021] [Indexed: 11/06/2022]
Abstract
Stochastic phenomena are often described by Langevin equations, which serve as a mesoscopic model for microscopic dynamics. It has been known since the work of Parisi and Sourlas that reversible (or equilibrium) dynamics present supersymmetries (SUSYs). These are revealed when the path-integral action is written as a function not only of the physical fields, but also of Grassmann fields representing a Jacobian arising from the noise distribution. SUSYs leave the action invariant upon a transformation of the fields that mixes the physical and the Grassmann ones. We show that contrary to common belief, it is possible to extend the known reversible construction to the case of arbitrary irreversible dynamics, for overdamped Langevin equations with additive white noise-provided their steady state is known. The construction is based on the fact that the Grassmann representation of the functional determinant is not unique, and can be chosen so as to present a generalization of the Parisi-Sourlas SUSY. We show how such SUSYs are related to time-reversal symmetries and allow one to derive modified fluctuation-dissipation relations valid in nonequilibrium. We give as a concrete example the results for the Kardar-Parisi-Zhang equation.
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Affiliation(s)
- Bastien Marguet
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne, France.,Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - Elisabeth Agoritsas
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Léonie Canet
- Université Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France.,Institut Universitaire de France, 1 rue Descartes, 75005 Paris, France
| | - Vivien Lecomte
- Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
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22
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McClure JE, Berg S, Armstrong RT. Thermodynamics of fluctuations based on time-and-space averages. Phys Rev E 2021; 104:035106. [PMID: 34654200 DOI: 10.1103/physreve.104.035106] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2020] [Accepted: 06/23/2021] [Indexed: 11/07/2022]
Abstract
We develop nonequilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in nonergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate of entropy production is shown to be explicitly scale dependent when considered in this context. We show that while any stationary process can be represented as having zero entropy production, second law constraints due to the Clausius theorem are preserved due to the fact that heat and work are related based on conservation of energy. As a demonstration, we consider the energy dynamics for the Carnot cycle and for Maxwell's demon. We then consider nonstationary processes, applying time-and-space averages to characterize nonergodic effects in heterogeneous systems where energy barriers such as compositional gradients are present. We show that the derived theory can be used to understand the origins of anomalous diffusion phenomena in systems where Fick's law applies at small length scales, but not at large length scales. We further characterize fluctuations in capillary-dominated systems, which are nonstationary due to the irreversibility of cooperative events.
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Affiliation(s)
- James E McClure
- Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA
| | - Steffen Berg
- Shell Global Solutions International B.V., Grasweg 31, 1031HW Amsterdam, The Netherlands
| | - Ryan T Armstrong
- School of Minerals and Energy Resources Engineering, University of New South Wales, Sydney 2052, Australia
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23
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Asheichyk K, Fuchs M, Krüger M. Brownian systems perturbed by mild shear: comparing response relations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:405101. [PMID: 34139676 DOI: 10.1088/1361-648x/ac0c3c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2021] [Accepted: 06/17/2021] [Indexed: 06/12/2023]
Abstract
We present a comprehensive study of the linear response of interacting underdamped Brownian particles to simple shear flow. We collect six different routes for computing the response, two of which are based on the symmetry of the considered system and observable with respect to the shear axes. We include the extension of the Green-Kubo relation to underdamped cases, which shows two unexpected additional terms. These six computational methods are applied to investigate the relaxation of the response towards the steady state for different observables, where interesting effects due to interactions and a finite particle mass are observed. Moreover, we compare the different response relations in terms of their statistical efficiency, identifying their relative demand on experimental measurement time or computational resources in computer simulations. Finally, several measures of breakdown of linear response theory for larger shear rates are discussed.
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Affiliation(s)
- Kiryl Asheichyk
- 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
- Department of Theoretical Physics and Astrophysics, Belarusian State University, 5 Babruiskaya St., 220006 Minsk, Belarus
| | - Matthias Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
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24
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Jung G, Schmid F. Fluctuation-dissipation relations far from equilibrium: a case study. SOFT MATTER 2021; 17:6413-6425. [PMID: 34132298 PMCID: PMC8262459 DOI: 10.1039/d1sm00521a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 06/06/2021] [Indexed: 06/12/2023]
Abstract
Fluctuation-dissipation relations or "theorems" (FDTs) are fundamental for statistical physics and can be rigorously derived for equilibrium systems. Their applicability to non-equilibrium systems is, however, debated. Here, we simulate an active microrheology experiment, in which a spherical colloid is pulled with a constant external force through a fluid, creating near-equilibrium and far-from-equilibrium systems. We characterize the structural and dynamical properties of these systems, and reconstruct an effective generalized Langevin equation (GLE) for the colloid dynamics. Specifically, we test the validity of two FDTs: The first FDT relates the non-equilibrium response of a system to equilibrium correlation functions, and the second FDT relates the memory friction kernel in the GLE to the stochastic force. We find that the validity of the first FDT depends strongly on the strength of the external driving: it is fulfilled close to equilibrium and breaks down far from it. In contrast, we observe that the second FDT is always fulfilled. We provide a mathematical argument why this generally holds for memory kernels reconstructed from a deterministic Volterra equation for correlation functions, even for non-stationary non-equilibrium systems. Motivated by the Mori-Zwanzig formalism, we therefore suggest to impose an orthogonality constraint on the stochastic force, which is in fact equivalent to the validity of this Volterra equation. Such GLEs automatically satisfy the second FDT and are unique, which is desirable when using GLEs for coarse-grained modeling.
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Affiliation(s)
- Gerhard Jung
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria.
| | - Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany.
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25
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Lesnicki D, Gao CY, Limmer DT, Rotenberg B. On the molecular correlations that result in field-dependent conductivities in electrolyte solutions. J Chem Phys 2021; 155:014507. [PMID: 34241409 DOI: 10.1063/5.0052860] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Employing recent advances in response theory and nonequilibrium ensemble reweighting, we study the dynamic and static correlations that give rise to an electric field-dependent ionic conductivity in electrolyte solutions. We consider solutions modeled with both implicit and explicit solvents, with different dielectric properties, and at multiple concentrations. Implicit solvent models at low concentrations and small dielectric constants exhibit strongly field-dependent conductivities. We compare these results to Onsager-Wilson theory of the Wien effect, which provides a qualitatively consistent prediction at low concentrations and high static dielectric constants but is inconsistent away from these regimes. The origin of the discrepancy is found to be increased ion correlations under these conditions. Explicit solvent effects act to suppress nonlinear responses, yielding a weakly field-dependent conductivity over the range of physically realizable field strengths. By decomposing the relevant time correlation functions, we find that the insensitivity of the conductivity to the field results from the persistent frictional forces on the ions from the solvent. Our findings illustrate the utility of nonequilibrium response theory in rationalizing nonlinear transport behavior.
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Affiliation(s)
- Dominika Lesnicki
- Sorbonne Université, CNRS, Physico-Chimie des Electrolytes et Nanosystèmes Interfaciaux, Paris, France
| | - Chloe Y Gao
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physico-Chimie des Electrolytes et Nanosystèmes Interfaciaux, Paris, France
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26
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Golokolenov I, Guthrie A, Kafanov S, Pashkin YA, Tsepelin V. On the origin of the controversial electrostatic field effect in superconductors. Nat Commun 2021; 12:2747. [PMID: 33980842 PMCID: PMC8115342 DOI: 10.1038/s41467-021-22998-0] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Accepted: 03/30/2021] [Indexed: 11/09/2022] Open
Abstract
Superconducting quantum devices offer numerous applications, from electrical metrology and magnetic sensing to energy-efficient high-end computing and advanced quantum information processing. The key elements of quantum circuits are (single and double) Josephson junctions controllable either by electric current or magnetic field. The voltage control, commonly used in semiconductor-based devices via the electrostatic field effect, would be far more versatile and practical. Hence, the field effect recently reported in superconducting devices may revolutionise the whole field of superconductor electronics provided it is confirmed. Here we show that the suppression of the critical current attributed to the field effect, can be explained by quasiparticle excitations in the constriction of superconducting devices. Our results demonstrate that a miniscule leakage current between the gate and the constriction of devices perfectly follows the Fowler-Nordheim model of electron field emission from a metal electrode and injects quasiparticles with energies sufficient to weaken or even suppress superconductivity. A recent report on electrostatic field effect in superconducting devices provides a high potential for advanced quantum technology, but it remains controversial. Here, the authors report that the suppression of critical current, which was attributed to the field effect, can instead be explained by quasiparticle excitations in the constriction of superconducting devices.
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Affiliation(s)
- I Golokolenov
- Department of Physics, Lancaster University, Lancaster, UK.,P. L. Kapitza Institute for Physical Problems of RAS, Moscow, Russia.,National Research University Higher School of Economics, Moscow, Russia
| | - A Guthrie
- Department of Physics, Lancaster University, Lancaster, UK
| | - S Kafanov
- Department of Physics, Lancaster University, Lancaster, UK.
| | - Yu A Pashkin
- Department of Physics, Lancaster University, Lancaster, UK.
| | - V Tsepelin
- Department of Physics, Lancaster University, Lancaster, UK
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27
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Martin D, O'Byrne J, Cates ME, Fodor É, Nardini C, Tailleur J, van Wijland F. Statistical mechanics of active Ornstein-Uhlenbeck particles. Phys Rev E 2021; 103:032607. [PMID: 33862678 DOI: 10.1103/physreve.103.032607] [Citation(s) in RCA: 61] [Impact Index Per Article: 20.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2020] [Accepted: 12/23/2020] [Indexed: 06/12/2023]
Abstract
We study the statistical properties of active Ornstein-Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffices to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We study in detail the steady-state distribution of AOUPs in the small persistence time limit and for spatially varying activity. At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. We characterize both the instability mechanism leading to phase separation and the resulting phase coexistence. We probe how, in the stationary state, AOUPs depart from their thermal equilibrium limit by investigating the emergence of ratchet currents and entropy production. In the small persistence time limit, we show how fluctuation-dissipation relations are recovered. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes.
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Affiliation(s)
- David Martin
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Jérémy O'Byrne
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Étienne Fodor
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Cesare Nardini
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Service de Physique de l'État Condensé, CNRS UMR 3680, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - Julien Tailleur
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Frédéric van Wijland
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
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28
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Zhang D, Ouyang Q. Nonequilibrium Thermodynamics in Biochemical Systems and Its Application. ENTROPY (BASEL, SWITZERLAND) 2021; 23:271. [PMID: 33668768 PMCID: PMC7996154 DOI: 10.3390/e23030271] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/31/2021] [Revised: 02/16/2021] [Accepted: 02/17/2021] [Indexed: 12/05/2022]
Abstract
Living systems are open systems, where the laws of nonequilibrium thermodynamics play the important role. Therefore, studying living systems from a nonequilibrium thermodynamic aspect is interesting and useful. In this review, we briefly introduce the history and current development of nonequilibrium thermodynamics, especially that in biochemical systems. We first introduce historically how people realized the importance to study biological systems in the thermodynamic point of view. We then introduce the development of stochastic thermodynamics, especially three landmarks: Jarzynski equality, Crooks' fluctuation theorem and thermodynamic uncertainty relation. We also summarize the current theoretical framework for stochastic thermodynamics in biochemical reaction networks, especially the thermodynamic concepts and instruments at nonequilibrium steady state. Finally, we show two applications and research paradigms for thermodynamic study in biological systems.
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Affiliation(s)
- Dongliang Zhang
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China;
| | - Qi Ouyang
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China;
- Center for Quantitative Biology and Peking-Tsinghua Center for Life Sciences, AAIC, Peking University, Beijing 100871, China
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29
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Lesnicki D, Gao CY, Rotenberg B, Limmer DT. Field-Dependent Ionic Conductivities from Generalized Fluctuation-Dissipation Relations. PHYSICAL REVIEW LETTERS 2020; 124:206001. [PMID: 32501100 DOI: 10.1103/physrevlett.124.206001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2019] [Revised: 03/18/2020] [Accepted: 04/21/2020] [Indexed: 06/11/2023]
Abstract
We derive a relationship for the electric field dependent ionic conductivity in terms of fluctuations of time integrated microscopic variables. We demonstrate this formalism with molecular dynamics simulations of solutions of differing ionic strength with implicit solvent conditions and molten salts. These calculations are aided by a novel nonequilibrium statistical reweighting scheme that allows for the conductivity to be computed as a continuous function of the applied field. In strong electrolytes, we find the fluctuations of the ionic current are Gaussian, and subsequently, the conductivity is constant with applied field. In weaker electrolytes and molten salts, we find the fluctuations of the ionic current are strongly non-Gaussian, and the conductivity increases with applied field. This nonlinear behavior, known phenomenologically for dilute electrolytes as the Onsager-Wien effect, is general and results from the suppression of ionic correlations at large applied fields, as we elucidate through both dynamic and static correlations within nonequilibrium steady states.
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Affiliation(s)
- Dominika Lesnicki
- Sorbonne Université, CNRS, Physico-Chimie des électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Chloe Y Gao
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physico-Chimie des électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
- Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, France
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Kavli Energy NanoScience Institute, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory., Berkeley, California 94720, USA
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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30
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Abstract
We present an approach to response around arbitrary out-of-equilibrium states in the form of a fluctuation-response inequality (FRI). We study the response of an observable to a perturbation of the underlying stochastic dynamics. We find that the magnitude of the response is bounded from above by the fluctuations of the observable in the unperturbed system and the Kullback-Leibler divergence between the probability densities describing the perturbed and the unperturbed system. This establishes a connection between linear response and concepts of information theory. We show that in many physical situations, the relative entropy may be expressed in terms of physical observables. As a direct consequence of this FRI, we show that for steady-state particle transport, the differential mobility is bounded by the diffusivity. For a "virtual" perturbation proportional to the local mean velocity, we recover the thermodynamic uncertainty relation (TUR) for steady-state transport processes. Finally, we use the FRI to derive a generalization of the uncertainty relation to arbitrary dynamics, which involves higher-order cumulants of the observable. We provide an explicit example, in which the TUR is violated but its generalization is satisfied with equality.
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Affiliation(s)
- Andreas Dechant
- Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan;
| | - Shin-Ichi Sasa
- Department of Physics 1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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31
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Netz RR. Approach to equilibrium and nonequilibrium stationary distributions of interacting many-particle systems that are coupled to different heat baths. Phys Rev E 2020; 101:022120. [PMID: 32168558 DOI: 10.1103/physreve.101.022120] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Accepted: 01/23/2020] [Indexed: 06/10/2023]
Abstract
A Hamiltonian-based model of many harmonically interacting massive particles that are subject to linear friction and coupled to heat baths at different temperatures is used to study the dynamic approach to equilibrium and nonequilibrium stationary states. An equilibrium system is here defined as a system whose stationary distribution equals the Boltzmann distribution, the relation of this definition to the conditions of detailed balance and vanishing probability current is discussed both for underdamped as well as for overdamped systems. Based on the exactly calculated dynamic approach to the stationary distribution, the functional that governs this approach, which is called the free entropy S_{free}(t), is constructed. For the stationary distribution S_{free}(t) becomes maximal and its time derivative, the free entropy production S[over ̇]_{free}(t), is minimal and vanishes. Thus, S_{free}(t) characterizes equilibrium as well as nonequilibrium stationary distributions by their extremal and stability properties. For an equilibrium system, i.e., if all heat baths have the same temperature, the free entropy equals the negative free energy divided by temperature and thus corresponds to the Massieu function which was previously introduced in an alternative formulation of statistical mechanics. Using a systematic perturbative scheme for calculating velocity and position correlations in the overdamped massless limit, explicit results for few particles are presented: For two particles localization in position and momentum space is demonstrated in the nonequilibrium stationary state, indicative of a tendency to phase separate. For three elastically interacting particles heat flows from a particle coupled to a cold reservoir to a particle coupled to a warm reservoir if the third reservoir is sufficiently hot. This does not constitute a violation of the second law of thermodynamics, but rather demonstrates that a particle in such a nonequilibrium system is not characterized by an effective temperature which equals the temperature of the heat bath it is coupled to. Active particle models can be described in the same general framework, which thereby allows us to characterize their entropy production not only in the stationary state but also in the approach to the stationary nonequilibrium state. Finally, the connection to nonequilibrium thermodynamics formulations that include the reservoir entropy production is discussed.
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Affiliation(s)
- Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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32
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Dal Cengio S, Levis D, Pagonabarraga I. Linear Response Theory and Green-Kubo Relations for Active Matter. PHYSICAL REVIEW LETTERS 2019; 123:238003. [PMID: 31868450 DOI: 10.1103/physrevlett.123.238003] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Indexed: 05/12/2023]
Abstract
We address the question of how interacting active systems in a nonequilibrium steady state respond to an external perturbation. We establish an extended fluctuation-dissipation theorem for active Brownian particles (ABP), which highlights the role played by the local violation of detailed balance due to activity. By making use of a Markovian approximation we derive closed Green-Kubo expressions for the diffusivity and mobility of ABP and quantify the deviations from the Stokes-Einstein relation. We compute the linear response function to an external force using unperturbed simulations of ABP and compare the results with the analytical predictions of the transport coefficients. Our results show the importance of the interplay between activity and interactions in the departure from equilibrium linear response.
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Affiliation(s)
- Sara Dal Cengio
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E08028 Barcelona, Spain
| | - Demian Levis
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E08028 Barcelona, Spain
- CECAM Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
- UBICS University of Barcelona Institute of Complex Systems, Martí i Franquès 1, E08028 Barcelona, Spain
| | - Ignacio Pagonabarraga
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E08028 Barcelona, Spain
- CECAM Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
- UBICS University of Barcelona Institute of Complex Systems, Martí i Franquès 1, E08028 Barcelona, Spain
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33
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Van Vu T, Hasegawa Y. Uncertainty relations for underdamped Langevin dynamics. Phys Rev E 2019; 100:032130. [PMID: 31640023 DOI: 10.1103/physreve.100.032130] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Indexed: 11/07/2022]
Abstract
A trade-off between the precision of an arbitrary current and the dissipation, known as the thermodynamic uncertainty relation, has been investigated for various Markovian systems. Here, we study the thermodynamic uncertainty relation for underdamped Langevin dynamics. By employing information inequalities, we prove that for such systems, the relative fluctuation of a current at a steady state is constrained by both the entropy production and the average dynamical activity. We find that unlike what is the case for overdamped dynamics, the dynamical activity plays an important role in the bound. We illustrate our results with two systems, a single-well potential system and a periodically driven Brownian particle model, and numerically verify the inequalities.
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Affiliation(s)
- Tan Van Vu
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
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34
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Sarracino A, Vulpiani A. On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems. CHAOS (WOODBURY, N.Y.) 2019; 29:083132. [PMID: 31472486 DOI: 10.1063/1.5110262] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2019] [Accepted: 08/08/2019] [Indexed: 06/10/2023]
Abstract
We review generalized fluctuation-dissipation relations, which are valid under general conditions even in "nonstandard systems," e.g., out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suitable correlation functions computed in the unperturbed dynamics. In these relations, typically, one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in nonstandard cases, including driven granular media, systems with a multiscale structure, active matter, and systems showing anomalous diffusion.
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Affiliation(s)
- A Sarracino
- Dipartimento di Ingegneria, Università della Campania "L. Vanvitelli," via Roma 29, 81031 Aversa (CE), Italy
| | - A Vulpiani
- Dipartimento di Fisica, Università Sapienza-p.le A. Moro 2, 00185 Roma, Italy
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35
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Asheichyk K, Solon AP, Rohwer CM, Krüger M. Response of active Brownian particles to shear flow. J Chem Phys 2019; 150:144111. [DOI: 10.1063/1.5086495] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kiryl Asheichyk
- 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
| | - Alexandre P. Solon
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matiére Condensée, LPTMC, F-75005 Paris, France
| | - Christian M. Rohwer
- 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
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36
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Ahmed WW, Fodor É, Almonacid M, Bussonnier M, Verlhac MH, Gov N, Visco P, van Wijland F, Betz T. Active Mechanics Reveal Molecular-Scale Force Kinetics in Living Oocytes. Biophys J 2019; 114:1667-1679. [PMID: 29642036 PMCID: PMC5954280 DOI: 10.1016/j.bpj.2018.02.009] [Citation(s) in RCA: 55] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Revised: 02/05/2018] [Accepted: 02/08/2018] [Indexed: 11/27/2022] Open
Abstract
Active diffusion of intracellular components is emerging as an important process in cell biology. This process is mediated by complex assemblies of molecular motors and cytoskeletal filaments that drive force generation in the cytoplasm and facilitate enhanced motion. The kinetics of molecular motors have been precisely characterized in vitro by single molecule approaches, but their in vivo behavior remains elusive. Here, we study the active diffusion of vesicles in mouse oocytes, where this process plays a key role in nuclear positioning during development, and combine an experimental and theoretical framework to extract molecular-scale force kinetics (force, power stroke, and velocity) of the in vivo active process. Assuming a single dominant process, we find that the nonequilibrium activity induces rapid kicks of duration τ ∼ 300 μs resulting in an average force of F ∼ 0.4 pN on vesicles in in vivo oocytes, remarkably similar to the kinetics of in vitro myosin-V. Our results reveal that measuring in vivo active fluctuations allows extraction of the molecular-scale activity in agreement with single-molecule studies and demonstrates a mesoscopic framework to access force kinetics.
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Affiliation(s)
- Wylie W Ahmed
- Department of Physics, California State University, Fullerton, California; Laboratoire Physico-Chimie Curie, Institut Curie, PSL Research University, Paris, France; Sorbonne Universités, UPMC Université Paris 06, Paris, France.
| | - Étienne Fodor
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom; Laboratoire Matière et Systèmes Complexes, Université Paris Diderot, Paris, France
| | - Maria Almonacid
- CIRB, Collège de France, and CNRS-UMR7241 and INSERM-U1050, Équipe Labellisée Fondation pour la Recherche Médicale, Paris, France
| | - Matthias Bussonnier
- Laboratoire Physico-Chimie Curie, Institut Curie, PSL Research University, Paris, France; Sorbonne Universités, UPMC Université Paris 06, Paris, France
| | - Marie-Hélène Verlhac
- CIRB, Collège de France, and CNRS-UMR7241 and INSERM-U1050, Équipe Labellisée Fondation pour la Recherche Médicale, Paris, France
| | - Nir Gov
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Paolo Visco
- Laboratoire Matière et Systèmes Complexes, Université Paris Diderot, Paris, France
| | - Frédéric van Wijland
- Laboratoire Matière et Systèmes Complexes, Université Paris Diderot, Paris, France
| | - Timo Betz
- Laboratoire Physico-Chimie Curie, Institut Curie, PSL Research University, Paris, France; Sorbonne Universités, UPMC Université Paris 06, Paris, France; Institute of Cell Biology, Center for Molecular Biology of Inflammation, Cells-in-Motion Cluster of Excellence, Münster University, Münster, Germany
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37
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Kreten FH, Hoffmann C, Riveline D, Kruse K. Active bundles of polar and bipolar filaments. Phys Rev E 2018; 98:012413. [PMID: 30110807 DOI: 10.1103/physreve.98.012413] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2018] [Indexed: 11/07/2022]
Abstract
Bundles of actin filaments and molecular motors of the myosin family are a common subcellular organizational motif. Typically, such bundles are under contractile stress resulting from interactions between the filaments and the motors. This holds in particular for contractile rings that appear in the late stages of cell division in animal cells and that cleave the mother into two daughter cells. It was recently shown that myosin organizes into regularly spaced clusters along rings in mammalian cells, whereas myosin clusters in fission yeast travel along the perimeter of actomyosin rings [Wollrab et al., Nat. Commun. 7, 11860 (2016)2041-172310.1038/ncomms11860]. A mechanism based on the association of the structurally polar actin filaments into bipolar structures was shown to provide a common explanation for both observations. Here, we analyze the dynamics of this mechanism in detail. We find a rich phase diagram depending on the actomyosin interaction strength and the stability of the bipolar structures. The system can notably organize into traveling waves. Furthermore, we identify the nature of the bifurcations connecting the various patterns as parameters are changed. Finally, we report experimental patterns observed in cytokinetic rings in fission yeast and link them to solutions of our dynamic equations. Our analysis highlights the possible role played by local polarity sorting of actin filaments for the dynamics and functionality of actomyosin networks.
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Affiliation(s)
- F H Kreten
- Theoretische Physik, Universität des Saarlandes, 66123 Saarbrücken, Germany
| | - Ch Hoffmann
- Theoretische Physik, Universität des Saarlandes, 66123 Saarbrücken, Germany
| | - D Riveline
- Laboratory of Cell Physics ISIS/IGBMC, CNRS and University of Strasbourg, Strasbourg, France; Institut de Génétique et de Biologie Moléculaire et Cellulaire, Illkirch, France; Centre National de la Recherche Scientifique, UMR7104, Illkirch, France; Institut National de la Santé et de la Recherche Médicale, U964, Illkirch, France; and Université de Strasbourg, Illkirch, France
| | - K Kruse
- NCCR Chemical Biology, Departments of Biochemistry and Theoretical Physics, University of Geneva, 1211 Geneva, Switzerland
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38
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Osmanović D. Properties of Rouse polymers with actively driven regions. J Chem Phys 2018; 149:164911. [DOI: 10.1063/1.5045686] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Dino Osmanović
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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39
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Mierke CT, Sauer F, Grosser S, Puder S, Fischer T, Käs JA. The two faces of enhanced stroma: Stroma acts as a tumor promoter and a steric obstacle. NMR IN BIOMEDICINE 2018; 31:e3831. [PMID: 29215759 DOI: 10.1002/nbm.3831] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2017] [Revised: 07/24/2017] [Accepted: 08/16/2017] [Indexed: 06/07/2023]
Abstract
In addition to genetic, morphological and biochemical alterations in cells, a key feature of the malignant progression of cancer is the stroma, including cancer cell motility as well as the emergence of metastases. Our current knowledge with regard to the biophysically driven experimental approaches of cancer progression indicates that mechanical aberrations are major contributors to the malignant progression of cancer. In particular, the mechanical probing of the stroma is of great interest. However, the impact of the tumor stroma on cellular motility, and hence the metastatic cascade leading to the malignant progression of cancer, is controversial as there are two different and opposing effects within the stroma. On the one hand, the stroma can promote and enhance the proliferation, survival and migration of cancer cells through mechanotransduction processes evoked by fiber alignment as a result of increased stroma rigidity. This enables all types of cancer to overcome restrictive biological capabilities. On the other hand, as a result of its structural constraints, the stroma acts as a steric obstacle for cancer cell motility in dense three-dimensional extracellular matrices, when the pore size is smaller than the cell's nucleus. The mechanical properties of the stroma, such as the tissue matrix stiffness and the entire architectural network of the stroma, are the major players in providing the optimal environment for cancer cell migration. Thus, biophysical methods determining the mechanical properties of the stroma, such as magnetic resonance elastography, are critical for the diagnosis and prediction of early cancer stages. Fibrogenesis and cancer are tightly connected, as there is an elevated risk of cancer on cystic fibrosis or, subsequently, cirrhosis. This also applies to the subsequent metastatic process.
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Affiliation(s)
- Claudia Tanja Mierke
- Faculty of Physics and Earth Science, Peter Debye Institute of Soft Matter Physics, Biological Physics Division, University of Leipzig, Leipzig, Germany
| | - Frank Sauer
- Faculty of Physics and Earth Science, Peter Debye Institute of Soft Matter Physics, Biological Physics Division, University of Leipzig, Leipzig, Germany
- Faculty of Physics and Earth Science, Peter Debye Institute of Soft Matter Physics, Soft Matter Physics Division, University of Leipzig, Leipzig, Germany
| | - Steffen Grosser
- Faculty of Physics and Earth Science, Peter Debye Institute of Soft Matter Physics, Soft Matter Physics Division, University of Leipzig, Leipzig, Germany
| | - Stefanie Puder
- Faculty of Physics and Earth Science, Peter Debye Institute of Soft Matter Physics, Biological Physics Division, University of Leipzig, Leipzig, Germany
| | - Tony Fischer
- Faculty of Physics and Earth Science, Peter Debye Institute of Soft Matter Physics, Biological Physics Division, University of Leipzig, Leipzig, Germany
| | - Josef Alfons Käs
- Faculty of Physics and Earth Science, Peter Debye Institute of Soft Matter Physics, Soft Matter Physics Division, University of Leipzig, Leipzig, Germany
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40
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Thermodynamics of Superdiffusion Generated by Lévy-Wiener Fluctuating Forces. ENTROPY 2018; 20:e20090658. [PMID: 33265747 PMCID: PMC7513181 DOI: 10.3390/e20090658] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/05/2018] [Revised: 08/16/2018] [Accepted: 08/29/2018] [Indexed: 11/25/2022]
Abstract
Scale free Lévy motion is a generalized analogue of the Wiener process. Its time derivative extends the notion of “white noise” to non-Gaussian noise sources, and as such, it has been widely used to model natural signal variations described by an overdamped Langevin stochastic differential equation. Here, we consider the dynamics of an archetypal model: a Brownian-like particle is driven by external forces, and noise is represented by uncorrelated Lévy fluctuations. An unperturbed system of that form eventually attains a steady state which is uniquely determined by the set of parameter values. We show that the analyzed Markov process with the stability index α<2 violates the detailed balance, i.e., its stationary state is quantified by a stationary probability density and nonvanishing current. We discuss consequences of the non-Gibbsian character of the stationary state of the system and its impact on the general form of the fluctuation–dissipation theorem derived for weak external forcing.
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41
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Sheth J, Meenderink SWF, Quiñones PM, Bozovic D, Levine AJ. Nonequilibrium limit-cycle oscillators: Fluctuations in hair bundle dynamics. Phys Rev E 2018; 97:062411. [PMID: 30011516 DOI: 10.1103/physreve.97.062411] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2018] [Indexed: 11/07/2022]
Abstract
We develop a framework for the general interpretation of the stochastic dynamical system near a limit cycle. Such quasiperiodic dynamics are commonly found in a variety of nonequilibrium systems, including the spontaneous oscillations of hair cells of the inner ear. We demonstrate quite generally that in the presence of noise, the phase of the limit cycle oscillator will diffuse, while deviations in the directions locally orthogonal to that limit cycle will display the Lorentzian power spectrum of a damped oscillator. We identify two mechanisms by which these stochastic dynamics can acquire a complex frequency dependence and discuss the deformation of the mean limit cycle as a function of temperature. The theoretical ideas are applied to data obtained from spontaneously oscillating hair cells of the amphibian sacculus.
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Affiliation(s)
- Janaki Sheth
- Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA
| | - Sebastiaan W F Meenderink
- Auditory Research Center, Caruso Department of Otolaryngology, USC, Los Angeles, California 90033, USA
| | - Patricia M Quiñones
- Caruso Department of Otolaryngology, Keck School of Medicine, USC, Los Angeles, California 90033, USA
| | - Dolores Bozovic
- Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA.,California NanoSystems Institute, UCLA, Los Angeles, California 90095-1596, USA
| | - Alex J Levine
- Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA.,Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095-1596, USA.,Department of Biomathematics, UCLA, Los Angeles, California 90095-1596, USA
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42
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Gnesotto FS, Mura F, Gladrow J, Broedersz CP. Broken detailed balance and non-equilibrium dynamics in living systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:066601. [PMID: 29504517 DOI: 10.1088/1361-6633/aab3ed] [Citation(s) in RCA: 110] [Impact Index Per Article: 18.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.
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Affiliation(s)
- F S Gnesotto
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
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43
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Netz RR. Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium. J Chem Phys 2018; 148:185101. [DOI: 10.1063/1.5020654] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roland R. Netz
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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44
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Basu U, Helden L, Krüger M. Extrapolation to Nonequilibrium from Coarse-Grained Response Theory. PHYSICAL REVIEW LETTERS 2018; 120:180604. [PMID: 29775331 DOI: 10.1103/physrevlett.120.180604] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Revised: 02/12/2018] [Indexed: 06/08/2023]
Abstract
Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many-body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse-grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far-from-equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many-body systems. It is illustrated in a four-state model and in the near critical Ising model.
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Affiliation(s)
- Urna Basu
- SISSA-International School for Advanced Studies and INFN, 34136 Trieste, Italy
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Laurent Helden
- 2. Physikalisches Institut, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Matthias Krüger
- 4th Institute for Theoretical Physics, Universität Stuttgart, 70550 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
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45
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Wang SW. Inferring energy dissipation from violation of the fluctuation-dissipation theorem. Phys Rev E 2018; 97:052125. [PMID: 29906903 DOI: 10.1103/physreve.97.052125] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2017] [Indexed: 06/08/2023]
Abstract
The Harada-Sasa equality elegantly connects the energy dissipation rate of a moving object with its measurable violation of the Fluctuation-Dissipation Theorem (FDT). Although proven for Langevin processes, its validity remains unclear for discrete Markov systems whose forward and backward transition rates respond asymmetrically to external perturbation. A typical example is a motor protein called kinesin. Here we show generally that the FDT violation persists surprisingly in the high-frequency limit due to the asymmetry, resulting in a divergent FDT violation integral and thus a complete breakdown of the Harada-Sasa equality. A renormalized FDT violation integral still well predicts the dissipation rate when each discrete transition produces a small entropy in the environment. Our study also suggests a way to infer this perturbation asymmetry based on the measurable high-frequency-limit FDT violation.
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Affiliation(s)
- Shou-Wen Wang
- Beijing Computational Science Research Center, Beijing, 100094, China and Department of Engineering Physics, Tsinghua University, Beijing, 100086, China
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46
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Mercier de Lépinay L, Pigeau B, Besga B, Arcizet O. Eigenmode orthogonality breaking and anomalous dynamics in multimode nano-optomechanical systems under non-reciprocal coupling. Nat Commun 2018; 9:1401. [PMID: 29643362 PMCID: PMC5895839 DOI: 10.1038/s41467-018-03741-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2017] [Accepted: 03/09/2018] [Indexed: 12/02/2022] Open
Abstract
Thermal motion of nanomechanical probes directly impacts their sensitivities to external forces. Its proper understanding is therefore critical for ultimate force sensing. Here, we investigate a vectorial force field sensor: a singly-clamped nanowire oscillating along two quasi-frequency-degenerate transverse directions. Its insertion in a rotational optical force field couples its eigenmodes non-symmetrically, causing dramatic modifications of its mechanical properties. In particular, the eigenmodes lose their intrinsic orthogonality. We show that this circumstance is at the origin of an anomalous excess of noise and of a violation of the fluctuation dissipation relation. Our model, which quantitatively accounts for all observations, provides a novel modified version of the fluctuation dissipation theorem that remains valid in non-conservative rotational force fields, and that reveals the prominent role of non-axial mechanical susceptibilities. These findings help understand the intriguing properties of thermal fluctuations in non-reciprocally-coupled multimode systems. Understanding the dynamics of nanomechanical probes is important for improving high-sensitivity force field sensing. Here, the authors study the vibrations of a suspended nanowire in the presence of a rotational optical force field which breaks the orthogonality of the nanoresonator eigenmodes.
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Affiliation(s)
| | - Benjamin Pigeau
- Institut Néel, Université Grenoble Alpes - CNRS:UPR2940, 38042, Grenoble, France
| | - Benjamin Besga
- Institut Néel, Université Grenoble Alpes - CNRS:UPR2940, 38042, Grenoble, France
| | - Olivier Arcizet
- Institut Néel, Université Grenoble Alpes - CNRS:UPR2940, 38042, Grenoble, France.
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47
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Gingrich TR, Horowitz JM. Fundamental Bounds on First Passage Time Fluctuations for Currents. PHYSICAL REVIEW LETTERS 2017; 119:170601. [PMID: 29219443 DOI: 10.1103/physrevlett.119.170601] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2017] [Indexed: 05/10/2023]
Abstract
Current is a characteristic feature of nonequilibrium systems. In stochastic systems, these currents exhibit fluctuations constrained by the rate of dissipation in accordance with the recently discovered thermodynamic uncertainty relation. Here, we derive a conjugate uncertainty relationship for the first passage time to accumulate a fixed net current. More generally, we use the tools of large-deviation theory to simply connect current fluctuations and first passage time fluctuations in the limit of long times and large currents. With this connection, previously discovered symmetries and bounds on the large-deviation function for currents are readily transferred to first passage times.
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Affiliation(s)
- Todd R Gingrich
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, 400 Technology Square, Cambridge, Massachusetts 02139, USA
| | - Jordan M Horowitz
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, 400 Technology Square, Cambridge, Massachusetts 02139, USA
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48
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Bibó A, Károlyi G, Kovács M. Unrevealed part of myosin's powerstroke accounts for high efficiency of muscle contraction. Biochim Biophys Acta Gen Subj 2017; 1861:2325-2333. [DOI: 10.1016/j.bbagen.2017.05.024] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2017] [Revised: 05/02/2017] [Accepted: 05/24/2017] [Indexed: 11/30/2022]
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49
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Lee HK, Lahiri S, Park H. Nonequilibrium steady states in Langevin thermal systems. Phys Rev E 2017; 96:022134. [PMID: 28950478 DOI: 10.1103/physreve.96.022134] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2016] [Indexed: 06/07/2023]
Abstract
Equilibrium is characterized by its fundamental properties, such as the detailed balance, the fluctuation-dissipation relation, and no heat dissipation. Based on the stochastic thermodynamics, we show that these three properties are equivalent to each other in conventional Langevin thermal systems with microscopic reversibility. Thus, a conventional steady state has either all three properties (equilibrium) or none of them (nonequilibrium). In contrast, with velocity-dependent forces breaking the microscopic reversibility, we prove that the detailed balance and the fluctuation-dissipation relation mutually exclude each other, and no equivalence relation is possible between any two of the three properties. This implies that a steady state of Langevin systems with velocity-dependent forces may maintain some equilibrium properties but not all of them. Our results are illustrated with a few example systems.
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Affiliation(s)
- Hyun Keun Lee
- Department of Physics, Sungkyunkwan University, Suwon 16419, Korea
| | - Sourabh Lahiri
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Hyunggyu Park
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
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50
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Abstract
Thermal energy agitates all matter, and its competition with ordering tendencies is a fundamental organizing principle in the physical world; this observation suggests that an effective temperature might emerge when external energy input enhances agitation. However, despite the repeated proposal of this concept based on kinetics for various nonequilibrium systems, the value of an effective temperature as a thermodynamic control parameter has been unclear. Here, we introduce a two-component system of driven Janus colloids, such that collisions induced by external energy sources agitate the system, and we demonstrate quantitative agreement with hallmarks of statistical thermodynamics for binary phase behavior: the archetypal phase diagram with equilibrium critical exponents, Gaussian displacement distributions, and even capillarity. The significance is to demonstrate a class of dynamical conditions under which thermodynamic analysis extends quantitatively to systems that are decidedly nonequilibrium except that the effective temperature differs from the physical temperature.
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