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Tasnim F, Wolpert DH. Stochastic Thermodynamics of Multiple Co-Evolving Systems-Beyond Multipartite Processes. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1078. [PMID: 37510025 PMCID: PMC10378096 DOI: 10.3390/e25071078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Revised: 07/14/2023] [Accepted: 07/14/2023] [Indexed: 07/30/2023]
Abstract
Many dynamical systems consist of multiple, co-evolving subsystems (i.e., they have multiple degrees of freedom). Often, the dynamics of one or more of these subsystems will not directly depend on the state of some other subsystems, resulting in a network of dependencies governing the dynamics. How does this dependency network affect the full system's thermodynamics? Prior studies on the stochastic thermodynamics of multipartite processes have addressed this question by assuming that, in addition to the constraints of the dependency network, only one subsystem is allowed to change state at a time. However, in many real systems, such as chemical reaction networks or electronic circuits, multiple subsystems can-or must-change state together. Here, we investigate the thermodynamics of such composite processes, in which multiple subsystems are allowed to change state simultaneously. We first present new, strictly positive lower bounds on entropy production in composite processes. We then present thermodynamic uncertainty relations for information flows in composite processes. We end with strengthened speed limits for composite processes.
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Affiliation(s)
- Farita Tasnim
- Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - David H Wolpert
- Santa Fe Institute, Santa Fe, NM 87501, USA
- Complexity Science Hub, Josefstadter Straße 39, 1080 Vienna, Austria
- Center for Bio-Social Complex Systems, Arizona State University, Tempe, AZ 85287, USA
- International Center for Theoretical Physics, 34151 Trieste, Italy
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Koyuk T, Seifert U. Thermodynamic Uncertainty Relation in Interacting Many-Body Systems. PHYSICAL REVIEW LETTERS 2022; 129:210603. [PMID: 36461951 DOI: 10.1103/physrevlett.129.210603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Revised: 06/01/2022] [Accepted: 10/06/2022] [Indexed: 06/17/2023]
Abstract
The thermodynamic uncertainty relation (TUR) has been well studied for systems with few degrees of freedom. While, in principle, the TUR holds for more complex systems with many interacting degrees of freedom as well, little is known so far about its behavior in such systems. We analyze the TUR in the thermodynamic limit for mixtures of driven particles with short-range interactions. Our main result is an explicit expression for the optimal estimate of the total entropy production in terms of single-particle currents and correlations between two-particle currents. Quantitative results for various versions of a driven lattice gas demonstrate the practical implementation of this approach.
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Affiliation(s)
- Timur Koyuk
- 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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Wolpert DH. Strengthened second law for multi-dimensional systems coupled to multiple thermodynamic reservoirs. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20200428. [PMID: 35599569 PMCID: PMC9125225 DOI: 10.1098/rsta.2020.0428] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
The second law of thermodynamics can be formulated as a restriction on the evolution of the entropy of any system undergoing Markovian dynamics. Here I show that this form of the second law is strengthened for multi-dimensional, complex systems, coupled to multiple thermodynamic reservoirs, if we have a set of a priori constraints restricting how the dynamics of each coordinate can depend on the other coordinates. As an example, this strengthened second law (SSL) applies to complex systems composed of multiple physically separated, co-evolving subsystems, each identified as a coordinate of the overall system. In this example, the constraints concern how the dynamics of some subsystems are allowed to depend on the states of the other subsystems. Importantly, the SSL applies to such complex systems even if some of its subsystems can change state simultaneously, which is prohibited in a multipartite process. The SSL also strengthens previously derived bounds on how much work can be extracted from a system using feedback control, if the system is multi-dimensional. Importantly, the SSL does not require local detailed balance. So it potentially applies to complex systems ranging from interacting economic agents to co-evolving biological species. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- David H. Wolpert
- Santa Fe Institute, Santa Fe, NM, USA
- Complexity Science Hub, Vienna, Arizona State University, Tempe, AZ, USA
- International Center for Theoretical Physics, Italy
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Wolpert DH. Strengthened second law for multi-dimensional systems coupled to multiple thermodynamic reservoirs. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022. [PMID: 35599569 DOI: 10.6084/m9.figshare.c.5896494] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The second law of thermodynamics can be formulated as a restriction on the evolution of the entropy of any system undergoing Markovian dynamics. Here I show that this form of the second law is strengthened for multi-dimensional, complex systems, coupled to multiple thermodynamic reservoirs, if we have a set of a priori constraints restricting how the dynamics of each coordinate can depend on the other coordinates. As an example, this strengthened second law (SSL) applies to complex systems composed of multiple physically separated, co-evolving subsystems, each identified as a coordinate of the overall system. In this example, the constraints concern how the dynamics of some subsystems are allowed to depend on the states of the other subsystems. Importantly, the SSL applies to such complex systems even if some of its subsystems can change state simultaneously, which is prohibited in a multipartite process. The SSL also strengthens previously derived bounds on how much work can be extracted from a system using feedback control, if the system is multi-dimensional. Importantly, the SSL does not require local detailed balance. So it potentially applies to complex systems ranging from interacting economic agents to co-evolving biological species. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- David H Wolpert
- Santa Fe Institute, Santa Fe, NM, USA
- Complexity Science Hub, Vienna, Arizona State University, Tempe, AZ, USA
- International Center for Theoretical Physics, Italy
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Da Costa L, Friston K, Heins C, Pavliotis GA. Bayesian mechanics for stationary processes. Proc Math Phys Eng Sci 2022; 477:20210518. [PMID: 35153603 PMCID: PMC8652275 DOI: 10.1098/rspa.2021.0518] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Accepted: 10/27/2021] [Indexed: 01/02/2023] Open
Abstract
This paper develops a Bayesian mechanics for adaptive systems. Firstly, we model the interface between a system and its environment with a Markov blanket. This affords conditions under which states internal to the blanket encode information about external states. Second, we introduce dynamics and represent adaptive systems as Markov blankets at steady state. This allows us to identify a wide class of systems whose internal states appear to infer external states, consistent with variational inference in Bayesian statistics and theoretical neuroscience. Finally, we partition the blanket into sensory and active states. It follows that active states can be seen as performing active inference and well-known forms of stochastic control (such as PID control), which are prominent formulations of adaptive behaviour in theoretical biology and engineering.
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Affiliation(s)
- Lancelot Da Costa
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK.,Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, UK
| | - Karl Friston
- Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, UK
| | - Conor Heins
- Department of Collective Behaviour, Max Planck Institute of Animal Behavior, Konstanz D-78457, Germany.,Centre for the Advanced Study of Collective Behaviour, University of Konstanz, Konstanz D-78457, Germany.,Department of Biology, University of Konstanz, Konstanz D-78457, Germany
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Kolchinsky A, Wolpert DH. Entropy production given constraints on the energy functions. Phys Rev E 2021; 104:034129. [PMID: 34654169 DOI: 10.1103/physreve.104.034129] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 08/25/2021] [Indexed: 11/07/2022]
Abstract
We consider the problem of driving a finite-state classical system from some initial distribution p to some final distribution p^{'} with vanishing entropy production (EP), under the constraint that the driving protocols can only use some limited set of energy functions E. Assuming no other constraints on the driving protocol, we derive a simple condition that guarantees that such a transformation can be carried out, which is stated in terms of the smallest probabilities in {p,p^{'}} and a graph-theoretic property defined in terms of E. Our results imply that a surprisingly small amount of control over the energy function is sufficient (in particular, any transformation p→p^{'} can be carried out as soon as one can control some one-dimensional parameter of the energy function, e.g., the energy of a single state). We also derive a lower bound on the EP under more general constraints on the transition rates, which is formulated in terms of a convex optimization problem.
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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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Yoshimura K, Ito S. Thermodynamic Uncertainty Relation and Thermodynamic Speed Limit in Deterministic Chemical Reaction Networks. PHYSICAL REVIEW LETTERS 2021; 127:160601. [PMID: 34723601 DOI: 10.1103/physrevlett.127.160601] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 09/09/2021] [Indexed: 06/13/2023]
Abstract
We generalize the thermodynamic uncertainty relation (TUR) and thermodynamic speed limit (TSL) for deterministic chemical reaction networks (CRNs). The scaled diffusion coefficient derived by considering the connection between macro- and mesoscopic CRNs plays an essential role in our results. The TUR shows that the product of the entropy production rate and the ratio of the scaled diffusion coefficient to the square of the rate of concentration change is bounded below by two. The TSL states a trade-off relation between speed and thermodynamic quantities, the entropy production, and the time-averaged scaled diffusion coefficient. The results are proved under the general setting of open and nonideal CRNs.
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Affiliation(s)
- Kohei Yoshimura
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0031, Japan
| | - Sosuke Ito
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0031, Japan
- JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
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