1
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Remlein B, Seifert U. Optimality of nonconservative driving for finite-time processes with discrete states. Phys Rev E 2021; 103:L050105. [PMID: 34134247 DOI: 10.1103/physreve.103.l050105] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Accepted: 05/11/2021] [Indexed: 11/07/2022]
Abstract
An optimal finite-time process drives a given initial distribution to a given final one in a given time at the lowest cost as quantified by total entropy production. We prove that for a system with discrete states this optimal process involves nonconservative driving, i.e., a genuine driving affinity, in contrast to the case of a system with continuous states. In a multicyclic network, the optimal driving affinity is bounded by the number of states within each cycle. If the driving affects forward and backwards rates nonsymmetrically, the bound additionally depends on a structural parameter characterizing this asymmetry.
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Affiliation(s)
- Benedikt Remlein
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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2
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Wang Y. Sub-Gaussian and subexponential fluctuation-response inequalities. Phys Rev E 2020; 102:052105. [PMID: 33327146 DOI: 10.1103/physreve.102.052105] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2020] [Accepted: 10/12/2020] [Indexed: 11/07/2022]
Abstract
Sub-Gaussian and subexponential distributions are introduced and applied to study the fluctuation-response relation out of equilibrium. A bound on the difference in expected values of an arbitrary sub-Gaussian or subexponential physical quantity is established in terms of its sub-Gaussian or subexponential norm. Based on that, we find that the entropy difference between two states is bounded by the energy fluctuation in these states. Moreover, we obtain generalized versions of the thermodynamic uncertainty relation in different regimes. Operational issues concerning the application of our results in an experimental setting are also addressed, and nonasymptotic bounds on the errors incurred by using the sample mean instead of the expected value in our fluctuation-response inequalities are derived.
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Affiliation(s)
- Yan Wang
- Department of Statistics, Iowa State University, Ames, Iowa 50011, USA
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3
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Ciccotti G, Rondoni L. Jarzynski on work and free energy relations: The case of variable volume. AIChE J 2020. [DOI: 10.1002/aic.17082] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Giovanni Ciccotti
- Istituto per le Applicazioni del Calcolo ‘Mauro Picone’ IAC‐CNR Roma Italy
- Dipartimento di Fisica Universit'a di Roma ‘La Sapienza’ Roma Italy
- School of Physics University College Dublin (UCD) Dublin Ireland
| | - Lamberto Rondoni
- Dipartimento di Scienze Matematiche Politecnico di Torino Torino Italy
- INFN, Sezione di Torino Torino Italy
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4
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Plata CA, Guéry-Odelin D, Trizac E, Prados A. Finite-time adiabatic processes: Derivation and speed limit. Phys Rev E 2020; 101:032129. [PMID: 32289944 DOI: 10.1103/physreve.101.032129] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2019] [Accepted: 03/03/2020] [Indexed: 11/07/2022]
Abstract
Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finite-time adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant at both the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression or decompression situation.
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Affiliation(s)
- Carlos A Plata
- Dipartimento di Fisica e Astronomia "Galileo Galilei," Istituto Nazionale di Fisica Nucleare, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - David Guéry-Odelin
- Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université de Toulouse, CNRS, UPS, Toulouse, France
| | | | - Antonio Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
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5
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Salazar DSP. Work distribution in thermal processes. Phys Rev E 2020; 101:030101. [PMID: 32289888 DOI: 10.1103/physreve.101.030101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Accepted: 02/20/2020] [Indexed: 06/11/2023]
Abstract
We find the moment generating function (mgf) of the nonequilibrium work for open systems undergoing a thermal process, i.e., when the stochastic dynamics maps thermal states into time-dependent thermal states. The mgf is given in terms of a temperaturelike scalar satisfying a first-order ordinary differential equation. We apply the result to some paradigmatic situations: a levitated nanoparticle in a breathing optical trap, a Brownian particle in a box with a moving piston, and a two-state system driven by an external field, where the work mgfs are obtained for different timescales and compared with Monte Carlo simulations.
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Affiliation(s)
- Domingos S P Salazar
- Unidade Acadêmica de Educação a Distância e Tecnologia, Universidade Federal Rural de Pernambuco, Recife, Pernambuco 52171-900, Brazil
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6
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Salazar DSP, Lira SA. Stochastic thermodynamics of nonharmonic oscillators in high vacuum. Phys Rev E 2019; 99:062119. [PMID: 31330744 DOI: 10.1103/physreve.99.062119] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2018] [Indexed: 06/10/2023]
Abstract
We perform an analytic study on the stochastic thermodynamics of a small classical particle trapped in a time-dependent single-well potential in the highly underdamped limit. It is shown that the nonequilibrium probability density function for the system's energy is a Maxwell-Boltzmann distribution (as in equilibrium) with a closed form time-dependent effective temperature and fractional degrees of freedom. We also find that the solvable model satisfies the Crooks fluctuation theorem, as expected. Moreover, we compute the average work in this isothermal process and characterize analytically the optimal protocol for minimum work. The optimal protocol presents an initial and a final jump which correspond to adiabatic processes linked by a smooth exponential time-dependent part for all kinds of single-well potentials. Furthermore, we argue that this result connects two distinct relevant experimental setups for trapped nanoparticles, the levitated particle in a harmonic trap, and the free particle in a box, as they are limiting cases of the general single-well potential and display the time-dependent optimal protocols. Finally, we highlight the connection between our system and an equivalent model of a gas of Brownian particles.
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Affiliation(s)
- Domingos S P Salazar
- Unidade Acadêmica de Educacão a Distância e Tecnologia, Universidade Federal Rural de Pernambuco, Recife, Pernambuco 52171-900 Brazil
| | - Sérgio A Lira
- Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-900 Brazil
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7
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Abstract
Biochemical and structural data reveal important aspects of the properties and function of a protein disulphide bond. Molecular dynamics simulations can complement this experimental data and can yield valuable insights into the dynamical behavior of the disulphide bond within the protein environment. Due to the increasing accuracy of the underlying energetic description and the increasing computational power at hand, such simulations have now reached a level, at which they can also make quantitative and experimentally testable predictions. We here give an overview of the computational methods used to predict functional aspects of protein disulphides, including the prestress, protein allosteric effects upon thiol/disulphide exchange, and disulphide redox potentials. We then outline in detail the use of free-energy perturbation methods to calculate the redox potential of a protein disulphide bond of interest. In a step-by-step protocol, we describe the workflow within the MD suite Gromacs, including practical advice on the simulation setup and choice of parameters. For other disulphide-related simulation methods, we refer to resources available online.
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Affiliation(s)
- Frauke Gräter
- Heidelberg Institute for Theoretical Studies, Heidelberg, Germany. .,Interdisciplinary Center for Scientific Computing, Heidelberg University, Heidelberg, Germany.
| | - Wenjin Li
- Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong, People's Republic of China
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8
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Arrar M, Boubeta FM, Szretter ME, Sued M, Boechi L, Rodriguez D. On the accurate estimation of free energies using the jarzynski equality. J Comput Chem 2018; 40:688-696. [DOI: 10.1002/jcc.25754] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2018] [Revised: 06/18/2018] [Accepted: 09/03/2018] [Indexed: 11/09/2022]
Affiliation(s)
- Mehrnoosh Arrar
- Instituto de Química-Física de los Materiales, Medio Ambiente y Energía, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina, Departamento de Química Inorgánica, Analítica y Química Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
| | - Fernando Martín Boubeta
- Instituto de Química-Física de los Materiales, Medio Ambiente y Energía, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina, Departamento de Química Inorgánica, Analítica y Química Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
| | - Maria Eugenia Szretter
- Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina, Instituto de Cálculo, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
| | - Mariela Sued
- Instituto de Cálculo, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
| | - Leonardo Boechi
- Instituto de Cálculo, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
| | - Daniela Rodriguez
- Instituto de Cálculo, CONICET-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires; Buenos Aires Argentina
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9
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Yunger Halpern N, Garner AJP, Dahlsten OCO, Vedral V. Maximum one-shot dissipated work from Rényi divergences. Phys Rev E 2018; 97:052135. [PMID: 29906852 DOI: 10.1103/physreve.97.052135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2017] [Indexed: 06/08/2023]
Abstract
Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, to a relative entropy between quantum states, and to a relative entropy between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity Rényi divergence is proportional to the maximum possible dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics.
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Affiliation(s)
- Nicole Yunger Halpern
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
| | - Andrew J P Garner
- Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Center for Quantum Technologies, National University of Singapore 117543, Republic of Singapore
| | - Oscar C O Dahlsten
- Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- London Institute for Mathematical Sciences, 35a South Street, Mayfair, London W1K 2XF, United Kingdom
| | - Vlatko Vedral
- Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Center for Quantum Technologies, National University of Singapore 117543, Republic of Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542
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10
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Bhattacharjee JK, Kirkpatrick TR, Sengers JV. Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations. Phys Rev E 2018; 97:042109. [PMID: 29758598 DOI: 10.1103/physreve.97.042109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2017] [Indexed: 06/08/2023]
Abstract
Work fluctuations and work probability distributions are fundamentally different in systems with short-ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with short-ranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet, well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behavior of the work probability distribution and the associated fluctuations is presented.
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Affiliation(s)
- J K Bhattacharjee
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
- Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - T R Kirkpatrick
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - J V Sengers
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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11
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Kirkpatrick TR, Bhattacherjee JK, Sengers JV. Contrasting Work Fluctuations and Distributions in Systems with Short-Range and Long-Range Correlations. PHYSICAL REVIEW LETTERS 2017; 119:030603. [PMID: 28777615 DOI: 10.1103/physrevlett.119.030603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2017] [Indexed: 06/07/2023]
Abstract
It is shown that the work fluctuations and work distribution functions are fundamentally different in systems with short-range versus long-range correlations. The two cases considered with long-range correlations are magnetic work fluctuations in an equilibrium isotropic ferromagnet and work fluctuations in a nonequilibrium fluid with a temperature gradient. The long-range correlations in the former case are due to equilibrium Goldstone modes, while in the latter they are due to generic nonequilibrium effects. The magnetic case is of particular interest, since an external magnetic field can be used to tune the system from one with long-range correlations to one with only short-range correlations. It is shown that in systems with long-range correlations the work distribution is extraordinarily broad compared to systems with only short-range correlations. Surprisingly, these results imply that fluctuation theorems such as the Jarzynski fluctuation theorem are more useful in systems with long-range correlations than in systems with short-range correlations.
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Affiliation(s)
- T R Kirkpatrick
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - J K Bhattacherjee
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
- Harish-Chandra Research Institute, Allahabad 211019, India
| | - J V Sengers
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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12
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Martínez IA, Roldán É, Dinis L, Rica RA. Colloidal heat engines: a review. SOFT MATTER 2016; 13:22-36. [PMID: 27477856 DOI: 10.1039/c6sm00923a] [Citation(s) in RCA: 71] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Stochastic heat engines can be built using colloidal particles trapped using optical tweezers. Here we review recent experimental realizations of microscopic heat engines. We first revisit the theoretical framework of stochastic thermodynamics that allows to describe the fluctuating behavior of the energy fluxes that occur at mesoscopic scales, and then discuss recent implementations of the colloidal equivalents to the macroscopic Stirling, Carnot and steam engines. These small-scale motors exhibit unique features in terms of power and efficiency fluctuations that have no equivalent in the macroscopic world. We also consider a second pathway for work extraction from colloidal engines operating between active bacterial reservoirs at different temperatures, which could significantly boost the performance of passive heat engines at the mesoscale. Finally, we provide some guidance on how the work extracted from colloidal heat engines can be used to generate net particle or energy currents, proposing a new generation of experiments with colloidal systems.
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Affiliation(s)
- Ignacio A Martínez
- Laboratoire de Physique, École Normale Supérieure, CNRS UMR5672, 46 Allée d'Italie, 69364 Lyon, France
| | - Édgar Roldán
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer strasse 38, 01187 Dresden, Germany and GISC - Grupo Interdisciplinar de Sistemas Complejos, Madrid, Spain
| | - Luis Dinis
- GISC - Grupo Interdisciplinar de Sistemas Complejos, Madrid, Spain and Departamento de Fisica Atómica, Molecular y Nuclear, Universidad Complutense Madrid, 28040 Madrid, Spain
| | - Raúl A Rica
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.
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13
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Kirkpatrick TR, Dorfman JR, Sengers JV. Work, work fluctuations, and the work distribution in a thermal nonequilibrium steady state. Phys Rev E 2016; 94:052128. [PMID: 27967150 DOI: 10.1103/physreve.94.052128] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2016] [Indexed: 11/07/2022]
Abstract
Long-ranged correlations generically exist in nonequilibrium fluid systems. In the case of a nonequilibrium steady state caused by a temperature gradient, the correlations are especially long-ranged and strong. The anomalous light scattering predicted to exist in these systems is well-confirmed by numerous experiments. Recently, the Casimir force or pressure due to these fluctuations or correlations has been discussed in great detail. In this paper, the notion of a Casimir work is introduced, and an alternative way to measure the nonequilibrium Casimir force is suggested. In particular, the nonequilibrium Casimir force is related to nonequilibrium heat, and not, as in equilibrium, to a volume derivative of an average energy. The nonequilibrium work fluctuations are determined and shown to be very anomalous compared to equilibrium work fluctuations. The nonequilibrium work distribution is also computed, and it is contrasted with work distributions in systems with short-range correlations. Again, there is a striking difference in the two cases. Formal theories of work and work distributions in nonequilibrium steady states are not explicit enough to illustrate any of these interesting features.
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Affiliation(s)
- T R Kirkpatrick
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - J R Dorfman
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - J V Sengers
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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14
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Gong Z, Lan Y, Quan HT. Stochastic Thermodynamics of a Particle in a Box. PHYSICAL REVIEW LETTERS 2016; 117:180603. [PMID: 27835006 DOI: 10.1103/physrevlett.117.180603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2016] [Indexed: 06/06/2023]
Abstract
The piston system (particles in a box) is the simplest paradigmatic model in traditional thermodynamics. However, the recently established framework of stochastic thermodynamics (ST) fails to apply to this model system due to the embedded singularity in the potential. In this Letter, we study the ST of a particle in a box by adopting a novel coordinate transformation technique. Through comparing with the exact solution of a breathing harmonic oscillator, we obtain analytical results of work distribution for an arbitrary protocol in the linear response regime and verify various predictions of the fluctuation-dissipation relation. When applying to the Brownian Szilard engine model, we obtain the optimal protocol λ_{t}=λ_{0}2^{t/τ} for a given sufficiently long total time τ. Our study not only establishes a paradigm for studying ST of a particle in a box but also bridges the long-standing gap in the development of ST.
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Affiliation(s)
- Zongping Gong
- School of Physics, Peking University, Beijing 100871, China
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Yueheng Lan
- Department of Physics, Beijing University of Posts and Telecommunications, Beijing 100876, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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15
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Yunger Halpern N, Jarzynski C. Number of trials required to estimate a free-energy difference, using fluctuation relations. Phys Rev E 2016; 93:052144. [PMID: 27300866 DOI: 10.1103/physreve.93.052144] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2016] [Indexed: 06/06/2023]
Abstract
The difference ΔF between free energies has applications in biology, chemistry, and pharmacology. The value of ΔF can be estimated from experiments or simulations, via fluctuation theorems developed in statistical mechanics. Calculating the error in a ΔF estimate is difficult. Worse, atypical trials dominate estimates. How many trials one should perform was estimated roughly by Jarzynski [Phys. Rev. E 73, 046105 (2006)PLEEE81539-375510.1103/PhysRevE.73.046105]. We enhance the approximation with the following information-theoretic strategies. We quantify "dominance" with a tolerance parameter chosen by the experimenter or simulator. We bound the number of trials one should expect to perform, using the order-∞ Rényi entropy. The bound can be estimated if one implements the "good practice" of bidirectionality, known to improve estimates of ΔF. Estimating ΔF from this number of trials leads to an error that we bound approximately. Numerical experiments on a weakly interacting dilute classical gas support our analytical calculations.
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Affiliation(s)
- Nicole Yunger Halpern
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
| | - Christopher Jarzynski
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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16
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Landi GT, Karevski D. Fluctuations of the heat exchanged between two quantum spin chains. Phys Rev E 2016; 93:032122. [PMID: 27078307 DOI: 10.1103/physreve.93.032122] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2014] [Indexed: 11/07/2022]
Abstract
The statistics of the heat exchanged between two quantum XX spin chains prepared at different temperatures is studied within the assumption of weak coupling. This provides simple formulas for the average heat and its corresponding characteristic function, from which the probability distribution may be computed numerically. These formulas are valid for arbitrary sizes and therefore allow us to analyze the role of the thermodynamic limit in this nonequilibrium setting. It is found that all thermodynamic quantities are extremely sensitive to the quantum phase transition of the XX chain.
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Affiliation(s)
| | - Dragi Karevski
- Institut Jean Lamour, Department P2M, Groupe de Physique Statistique, Université de Lorraine, CNRS, B.P. 70239, F-54506 Vandoeuvre les Nancy Cedex, France
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17
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Martínez IA, Roldán É, Dinis L, Petrov D, Parrondo JMR, Rica RA. Brownian Carnot engine. NATURE PHYSICS 2016; 12:67-70. [PMID: 27330541 PMCID: PMC4907353 DOI: 10.1038/nphys3518] [Citation(s) in RCA: 155] [Impact Index Per Article: 19.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2015] [Accepted: 09/16/2015] [Indexed: 05/23/2023]
Abstract
The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths1. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors2 and some artificial micro-engines3-5 operate. As described by stochastic thermodynamics6,7, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit8. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures9-11. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency-an insight that could inspire new strategies in the design of efficient nano-motors.
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Affiliation(s)
- I. A. Martínez
- ICFO-Institut de Ciències Fotòniques, Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Laboratoire de Physique, École Normale Supérieure, CNRS UMR5672 46 Allée d’Italie, 69364 Lyon, France
| | - É. Roldán
- ICFO-Institut de Ciències Fotòniques, Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
- GISC-Grupo Interdisciplinar de Sistemas Complejos, 28040 Madrid, Spain
| | - L. Dinis
- GISC-Grupo Interdisciplinar de Sistemas Complejos, 28040 Madrid, Spain
- Departamento de Fisica Atómica, Molecular y Nuclear, Universidad Complutense Madrid, 28040 Madrid, Spain
| | - D. Petrov
- ICFO-Institut de Ciències Fotòniques, Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - J. M. R. Parrondo
- GISC-Grupo Interdisciplinar de Sistemas Complejos, 28040 Madrid, Spain
- Departamento de Fisica Atómica, Molecular y Nuclear, Universidad Complutense Madrid, 28040 Madrid, Spain
| | - R. A. Rica
- ICFO-Institut de Ciències Fotòniques, Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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18
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Ford IJ, Eyre RW. Work relations for a system governed by Tsallis statistics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022143. [PMID: 26382379 DOI: 10.1103/physreve.92.022143] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2015] [Indexed: 06/05/2023]
Abstract
We derive analogs of the Jarzynski equality and Crooks relation to characterize the nonequilibrium work associated with changes in the spring constant of an overdamped oscillator in a quadratically varying spatial temperature profile. The stationary state of such an oscillator is described by Tsallis statistics, and the work relations for certain processes may be expressed in terms of q-exponentials. We suggest that these identities might be a feature of nonequilibrium processes in circumstances where Tsallis distributions are found.
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Affiliation(s)
- Ian J Ford
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Robert W Eyre
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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19
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Asgarani S. Families of Fokker-Planck equations and the associated entropic form for a distinct steady-state probability distribution with a known external force field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022104. [PMID: 25768455 DOI: 10.1103/physreve.91.022104] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2014] [Indexed: 06/04/2023]
Abstract
A method of finding entropic form for a given stationary probability distribution and specified potential field is discussed, using the steady-state Fokker-Planck equation. As examples, starting with the Boltzmann and Tsallis distribution and knowing the force field, we obtain the Boltzmann-Gibbs and Tsallis entropies. Also, the associated entropy for the gamma probability distribution is found, which seems to be in the form of the gamma function. Moreover, the related Fokker-Planck equations are given for the Boltzmann, Tsallis, and gamma probability distributions.
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Affiliation(s)
- Somayeh Asgarani
- Department of Physics, Payame Noor University, PO Box 19395-3697, Tehran, Iran
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20
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Gong Z, Deffner S, Quan HT. Interference of identical particles and the quantum work distribution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062121. [PMID: 25615058 DOI: 10.1103/physreve.90.062121] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2014] [Indexed: 06/04/2023]
Abstract
Quantum-mechanical particles in a confining potential interfere with each other while undergoing thermodynamic processes far from thermal equilibrium. By evaluating the corresponding transition probabilities between many-particle eigenstates we obtain the quantum work distribution function for identical bosons and fermions, which we compare with the case of distinguishable particles. We find that the quantum work distributions for bosons and fermions significantly differ at low temperatures, while, as expected, at high temperatures the work distributions converge to the classical expression. These findings are illustrated with two analytically solvable examples, namely the time-dependent infinite square well and the parametric harmonic oscillator.
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Affiliation(s)
- Zongping Gong
- School of Physics, Peking University, Beijing 100871, China
| | - Sebastian Deffner
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 USA and Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China and Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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21
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Mestres P, Martinez IA, Ortiz-Ambriz A, Rica RA, Roldan E. Realization of nonequilibrium thermodynamic processes using external colored noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032116. [PMID: 25314404 DOI: 10.1103/physreve.90.032116] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2014] [Indexed: 06/04/2023]
Abstract
We investigate the dynamics of single microparticles immersed in water that are driven out of equilibrium in the presence of an additional external colored noise. As a case study, we trap a single polystyrene particle in water with optical tweezers and apply an external electric field with flat spectrum but a finite bandwidth of the order of kHz. The intensity of the external noise controls the amplitude of the fluctuations of the position of the particle and therefore of its effective temperature. Here we show, in two different nonequilibrium experiments, that the fluctuations of the work done on the particle obey the Crooks fluctuation theorem at the equilibrium effective temperature, given that the sampling frequency and the noise cutoff frequency are properly chosen.
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Affiliation(s)
- Pau Mestres
- Institut de Ciències Fotòniques (ICFO), Mediterranean Technology Park, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels (Barcelona), Spain
| | - Ignacio A Martinez
- Institut de Ciències Fotòniques (ICFO), Mediterranean Technology Park, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels (Barcelona), Spain
| | - Antonio Ortiz-Ambriz
- Institut de Ciències Fotòniques (ICFO), Mediterranean Technology Park, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels (Barcelona), Spain and Photonics and Mathematical Optics Group, Tecnológico de Monterrey, 64849 Mexico
| | - Raul A Rica
- Institut de Ciències Fotòniques (ICFO), Mediterranean Technology Park, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels (Barcelona), Spain
| | - Edgar Roldan
- Institut de Ciències Fotòniques (ICFO), Mediterranean Technology Park, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels (Barcelona), Spain and Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
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22
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Quan HT. Maximum efficiency of ideal heat engines based on a small system: correction to the Carnot efficiency at the nanoscale. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062134. [PMID: 25019751 DOI: 10.1103/physreve.89.062134] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2014] [Indexed: 06/03/2023]
Abstract
We study the maximum efficiency of a heat engine based on a small system. It is revealed that due to the finiteness of the system, irreversibility may arise when the working substance contacts with a heat reservoir. As a result, there is a working-substance-dependent correction to the Carnot efficiency. We derive a general and simple expression for the maximum efficiency of a Carnot cycle heat engine in terms of the relative entropy. This maximum efficiency approaches the Carnot efficiency asymptotically when the size of the working substance increases to the thermodynamic limit. Our study extends Carnot's result of the maximum efficiency to an arbitrary working substance and elucidates the subtlety of thermodynamic laws in small systems.
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Affiliation(s)
- H T Quan
- School of Physics, Peking University, Beijing 100871, China and Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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23
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Boulougouris GC. Free energy calculations, enhanced by a Gaussian ansatz, for the "chemical work" distribution. J Comput Chem 2014; 35:1024-35. [PMID: 24664967 DOI: 10.1002/jcc.23590] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2013] [Revised: 01/18/2014] [Accepted: 02/26/2014] [Indexed: 01/09/2023]
Abstract
The evaluation of the free energy is essential in molecular simulation because it is intimately related with the existence of multiphase equilibrium. Recently, it was demonstrated that it is possible to evaluate the Helmholtz free energy using a single statistical ensemble along an entire isotherm by accounting for the "chemical work" of transforming each molecule, from an interacting one, to an ideal gas. In this work, we show that it is possible to perform such a free energy perturbation over a liquid vapor phase transition. Furthermore, we investigate the link between a general free energy perturbation scheme and the novel nonequilibrium theories of Crook's and Jarzinsky. We find that for finite systems away from the thermodynamic limit the second law of thermodynamics will always be an inequality for isothermal free energy perturbations, resulting always to a dissipated work that may tend to zero only in the thermodynamic limit. The work, the heat, and the entropy produced during a thermodynamic free energy perturbation can be viewed in the context of the Crooks and Jarzinsky formalism, revealing that for a given value of the ensemble average of the "irreversible" work, the minimum entropy production corresponded to a Gaussian distribution for the histogram of the work. We propose the evaluation of the free energy difference in any free energy perturbation based scheme on the average irreversible "chemical work" minus the dissipated work that can be calculated from the variance of the distribution of the logarithm of the work histogram, within the Gaussian approximation. As a consequence, using the Gaussian ansatz for the distribution of the "chemical work," accurate estimates for the chemical potential and the free energy of the system can be performed using much shorter simulations and avoiding the necessity of sampling the computational costly tails of the "chemical work." For a more general free energy perturbation scheme that the Gaussian ansatz may not be valid, the free energy calculation can be expressed in terms of the moment generating function of the "chemical work" distribution.
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Affiliation(s)
- Georgios C Boulougouris
- Department of Molecular Biology and Genetics, Democritius University, Alexandroupolis, 68100, Greece
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24
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Leonard T, Lander B, Seifert U, Speck T. Stochastic thermodynamics of fluctuating density fields: Non-equilibrium free energy differences under coarse-graining. J Chem Phys 2013; 139:204109. [DOI: 10.1063/1.4833136] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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25
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Subaşı Y, Jarzynski C. Microcanonical work and fluctuation relations for an open system: An exactly solvable model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042136. [PMID: 24229144 DOI: 10.1103/physreve.88.042136] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2013] [Indexed: 06/02/2023]
Abstract
We calculate the probability distribution of work for an exactly solvable model of a system interacting with its environment. The system of interest is a harmonic oscillator with a time-dependent control parameter, the environment is modeled by N-independent harmonic oscillators with arbitrary frequencies, and the system-environment coupling is bilinear and not necessarily weak. The initial conditions of the combined system and environment are sampled from a microcanonical distribution and the system is driven out of equilibrium by changing the control parameter according to a prescribed protocol. In the limit of infinitely large environment, i.e., N→∞, we recover the nonequilibrium work relation and Crooks's fluctuation relation. Moreover, the microcanonical Crooks relation is verified for finite environments. Finally, we show the equivalence of multitime correlation functions of the system in the infinite environment limit for canonical and microcanonical ensembles.
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Affiliation(s)
- Y Subaşı
- Joint Quantum Institute and Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA
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26
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27
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Echeverria I, Amzel LM. Estimation of Free-Energy Differences from Computed Work Distributions: An Application of Jarzynski’s Equality. J Phys Chem B 2012; 116:10986-95. [DOI: 10.1021/jp300527q] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ignacia Echeverria
- Department of Biophysics
and Biophysical Chemistry,
School of Medicine, Johns Hopkins University, Baltimore, Maryland 21205, United States
| | - L. Mario Amzel
- Department of Biophysics
and Biophysical Chemistry,
School of Medicine, Johns Hopkins University, Baltimore, Maryland 21205, United States
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28
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Davie SJ, Reid JC, Searles DJ. The free energy of expansion and contraction: Treatment of arbitrary systems using the Jarzynski equality. J Chem Phys 2012; 136:174111. [DOI: 10.1063/1.4707348] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Suárez A, Silbey R, Oppenheim I. Phase transition in the Jarzynski estimator of free energy differences. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051108. [PMID: 23004704 DOI: 10.1103/physreve.85.051108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2011] [Revised: 02/07/2012] [Indexed: 06/01/2023]
Abstract
The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in terms of the change in behavior of the Jarzynski estimator of equilibrium free energy differences from nonequilibrium work measurements. Given a fixed number of measurements, the Jarzynski estimator is unbiased for sufficiently small systems. In these systems the directionality of time is poorly defined and the configurations that dominate the empirical average, but which are in fact typical of the reverse process, are sufficiently well sampled. As the system size increases the arrow of time becomes better defined. The dominant atypical fluctuations become rare and eventually cannot be sampled with the limited resources that are available. Asymptotically, only typical work values are measured. The Jarzynski estimator becomes maximally biased and approaches the exponential of minus the average work, which is the result that is expected from standard macroscopic thermodynamics. In the proper scaling limit, this regime change has been recently described in terms of a phase transition in variants of the random energy model. In this paper this correspondence is further demonstrated in two examples of physical interest: the sudden compression of an ideal gas and adiabatic quasistatic volume changes in a dilute real gas.
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Affiliation(s)
- Alberto Suárez
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
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30
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Quan HT, Jarzynski C. Validity of nonequilibrium work relations for the rapidly expanding quantum piston. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031102. [PMID: 22587033 DOI: 10.1103/physreve.85.031102] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2011] [Indexed: 05/31/2023]
Abstract
Recent work by Teifel and Mahler [Eur. Phys. J. B 75, 275 (2010)] raises legitimate concerns regarding the validity of quantum nonequilibrium work relations in processes involving moving hard walls. We study this issue in the context of the rapidly expanding one-dimensional quantum piston. Utilizing exact solutions of the time-dependent Schrödinger equation, we find that the evolution of the wave function can be decomposed into static and dynamic components, which have simple semiclassical interpretations in terms of particle-piston collisions. We show that nonequilibrium work relations remain valid at any finite piston speed, provided both components are included, and we study explicitly the work distribution for this model system.
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Affiliation(s)
- H T Quan
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA
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31
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Chow KW. Logarithmic nonlinear Schrödinger equation and irrotational, compressible flows: an exact solution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:016308. [PMID: 21867305 DOI: 10.1103/physreve.84.016308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2011] [Revised: 05/12/2011] [Indexed: 05/31/2023]
Abstract
A class of irrotational, isentropic, and compressible flows is studied theoretically by formulating the density and the velocity potential in a Madelung transformation. The resulting nonlinear Schrödinger equation is solved in terms of similarity variables. One particular family of exact solutions, valid for any ratio of the specific heat capacities of the gas, permits explicit expressions of the fluid properties and velocities in terms of time and spatial coordinates. Analytically, the density is a Gaussian function of the similarity variable, while the temperature is a function of time only. This method is applicable in one (1D), two, and three dimensional geometries. As a simple example, a 1D gas column, with mass injection on one side and a steadily translating wall on the other, can be formulated exactly. The connection with the evolution of an unsteady velocity potential will also be examined.
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Affiliation(s)
- K W Chow
- Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong.
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32
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Kwon C, Noh JD, Park H. Nonequilibrium fluctuations for linear diffusion dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:061145. [PMID: 21797340 DOI: 10.1103/physreve.83.061145] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2011] [Indexed: 05/31/2023]
Abstract
We present the theoretical study on nonequilibrium (NEQ) fluctuations for diffusion dynamics in high dimensions driven by a linear drift force. We consider a general situation in which NEQ is caused by two conditions: (i) drift force not derivable from a potential function, and (ii) diffusion matrix not proportional to the unit matrix, implying nonidentical and correlated multidimensional noise. The former is a well-known NEQ source and the latter can be realized in the presence of multiple heat reservoirs or multiple noise sources. We develop a statistical mechanical theory based on generalized thermodynamic quantities such as energy, work, and heat. The NEQ fluctuation theorems are reproduced successfully. We also find the time-dependent probability distribution function exactly as well as the NEQ work production distribution P(W) in terms of solutions of nonlinear differential equations. In addition, we compute low-order cumulants of the NEQ work production explicitly. In two dimensions, we carry out numerical simulations to check out our analytic results and also to get P(W). We find an interesting dynamic phase transition in the exponential tail shape of P(W), associated with a singularity found in solutions of the nonlinear differential equation. Finally, we discuss possible realizations in experiments.
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Affiliation(s)
- Chulan Kwon
- Department of Physics, Myongji University, Yongin, Gyeonggi-Do , Republic of Korea.
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33
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Chatterjee D, Cherayil BJ. Exact path-integral evaluation of the heat distribution function of a trapped brownian oscillator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051104. [PMID: 21230434 DOI: 10.1103/physreve.82.051104] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2010] [Revised: 08/13/2010] [Indexed: 05/30/2023]
Abstract
Using path integrals, we derive an exact expression--valid at all times t--for the distribution P(Q,t) of the heat fluctuations Q of a brownian particle trapped in a stationary harmonic well. We find that P(Q,t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t→∞ exactly recovers the heat distribution function obtained recently by Imparato [Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen [Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q,t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q,t) for the case v=0 .
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Affiliation(s)
- Debarati Chatterjee
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India
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34
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Altland A, De Martino A, Egger R, Narozhny B. Fluctuation relations and rare realizations of transport observables. PHYSICAL REVIEW LETTERS 2010; 105:170601. [PMID: 21231031 DOI: 10.1103/physrevlett.105.170601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2010] [Revised: 08/24/2010] [Indexed: 05/30/2023]
Abstract
Fluctuation relations establish rigorous identities for the nonequilibrium averages of observables. Starting from a general transport master equation with time-dependent rates, we employ the stochastic path integral approach to study statistical fluctuations around such averages. We show how under nonequilibrium conditions, rare realizations of transport observables are crucial and imply massive fluctuations that may completely mask such identities. Quantitative estimates for these fluctuations are provided. We illustrate our results on the paradigmatic example of a mesoscopic RC circuit.
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35
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Goette M, Grubmüller H. Accuracy and convergence of free energy differences calculated from nonequilibrium switching processes. J Comput Chem 2009; 30:447-56. [DOI: 10.1002/jcc.21073] [Citation(s) in RCA: 72] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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36
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Maragakis P, Ritort F, Bustamante C, Karplus M, Crooks GE. Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise. J Chem Phys 2008; 129:024102. [PMID: 18624511 DOI: 10.1063/1.2937892] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Jarzynski equality and the fluctuation theorem relate equilibrium free energy differences to nonequilibrium measurements of the work. These relations extend to single-molecule experiments that have probed the finite-time thermodynamics of proteins and nucleic acids. The effects of experimental error and instrument noise have not been considered previously. Here, we present a Bayesian formalism for estimating free energy changes from nonequilibrium work measurements that compensates for instrument noise and combines data from multiple driving protocols. We reanalyze a recent set of experiments in which a single RNA hairpin is unfolded and refolded using optical tweezers at three different rates. Interestingly, the fastest and farthest-from-equilibrium measurements contain the least instrumental noise and, therefore, provide a more accurate estimate of the free energies than a few slow, more noisy, near-equilibrium measurements. The methods we propose here will extend the scope of single-molecule experiments; they can be used in the analysis of data from measurements with atomic force microscopy, optical, and magnetic tweezers.
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Affiliation(s)
- Paul Maragakis
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA.
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37
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Quan HT, Yang S, Sun CP. Microscopic work distribution of small systems in quantum isothermal processes and the minimal work principle. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021116. [PMID: 18850795 DOI: 10.1103/physreve.78.021116] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2008] [Revised: 06/15/2008] [Indexed: 05/26/2023]
Abstract
For a two-level quantum mechanical system, we derive microscopically the exact expression for the fluctuation of microscopic work in a multistep nonequilibrium process, and we rigorously prove that in an isothermal process, the fluctuation is vanishingly small and the most probabilistic work is just equal to the difference of the free energy. Our study demonstrates that the convergence of the microscopic work in the isothermal process is due to the nature of the isothermal process rather than the usual thermodynamic limit condition. Our investigation justifies the validity of a "minimum work principle" formulation of the second law even for a small system far from the thermodynamic limit.
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Affiliation(s)
- H T Quan
- Theoretical Division, MS B213, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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38
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Protein-protein interaction investigated by steered molecular dynamics: the TCR-pMHC complex. Biophys J 2008; 95:3575-90. [PMID: 18621828 DOI: 10.1529/biophysj.108.131383] [Citation(s) in RCA: 90] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We present a novel steered molecular dynamics scheme to induce the dissociation of large protein-protein complexes. We apply this scheme to study the interaction of a T cell receptor (TCR) with a major histocompatibility complex (MHC) presenting a peptide (p). Two TCR-pMHC complexes are considered, which only differ by the mutation of a single amino acid on the peptide; one is a strong agonist that produces T cell activation in vivo, while the other is an antagonist. We investigate the interaction mechanism from a large number of unbinding trajectories by analyzing van der Waals and electrostatic interactions and by computing energy changes in proteins and solvent. In addition, dissociation potentials of mean force are calculated with the Jarzynski identity, using an averaging method developed for our steering scheme. We analyze the convergence of the Jarzynski exponential average, which is hampered by the large amount of dissipative work involved and the complexity of the system. The resulting dissociation free energies largely underestimate experimental values, but the simulations are able to clearly differentiate between wild-type and mutated TCR-pMHC and give insights into the dissociation mechanism.
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39
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Ritort F. Nonequilibrium Fluctuations in Small Systems: From Physics to Biology. ADVANCES IN CHEMICAL PHYSICS 2008. [DOI: 10.1002/9780470238080.ch2] [Citation(s) in RCA: 85] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
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40
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Sung J. Application range of Jarzynski's equation for boundary-switching processes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:042101. [PMID: 18517669 DOI: 10.1103/physreve.77.042101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2007] [Revised: 02/23/2008] [Indexed: 05/26/2023]
Abstract
Jarzynski's equation (JE) has been known to relate free energy change of a system to statistical distribution of work done on the system for an arbitrary process. In the present work, we first establish the validity condition of JE for boundary switching processes. The validity condition of JE is examined for an example of spontaneous irreversible processes, for which, obviously, JE does not hold. We find that the free energy difference between two configurational states with different phase-space volume cannot be correctly estimated by JE for any adiabatic boundary switching process.
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Affiliation(s)
- Jaeyoung Sung
- Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea.
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41
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Weiss JB. Fluctuation properties of steady-state Langevin systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:061128. [PMID: 18233835 DOI: 10.1103/physreve.76.061128] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2007] [Indexed: 05/25/2023]
Abstract
Motivated by stochastic models of climate phenomena, the steady state of a linear stochastic model with additive Gaussian white noise is studied. Fluctuation theorems for nonequilibrium steady states provide a constraint on the character of these fluctuations. The properties of the fluctuations which are unconstrained by the fluctuation theorem are investigated and related to the model parameters. The irreversibility of trajectory segments, which satisfies a fluctuation theorem, is used as a measure of nonequilibrium fluctuations. The moments of the irreversibility probability density function (pdf) are found and the pdf is seen to be non-Gaussian. The average irreversibility goes to zero for short and long trajectory segments and has a maximum for some finite segment length, which defines a characteristic time scale of the fluctuations. The initial average irreversibility growth rate is equal to the average entropy production and is related to noise amplification. For systems with a separation of deterministic time scales, modes with time scales much shorter than the trajectory time span and whose noise amplitudes are not asymptotically large, do not, to first order, contribute to the irreversibility statistics, providing a potential basis for dimensional reduction.
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Affiliation(s)
- Jeffrey B Weiss
- Department of Atmospheric and Oceanic Sciences, University of Colorado, Boulder, CO 80309, USA.
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42
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Sung J. Theoretical test of Jarzynski's equality for reversible volume-switching processes of an ideal gas system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:012101. [PMID: 17677514 DOI: 10.1103/physreve.76.012101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2007] [Indexed: 05/16/2023]
Abstract
We present an exact theoretical test of Jarzynski's equality (JE) for reversible volume-switching processes of an ideal gas system. The exact analysis shows that the prediction of JE for the free energy difference is the same as the work done on the gas system during the reversible process that is dependent on the shape of path of the reversible volume-switching process.
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Affiliation(s)
- Jaeyoung Sung
- Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea.
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