1
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Pietzonka P, Coghi F. Thermodynamic cost for precision of general counting observables. Phys Rev E 2024; 109:064128. [PMID: 39020906 DOI: 10.1103/physreve.109.064128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 05/13/2024] [Indexed: 07/20/2024]
Abstract
We analytically derive universal bounds that describe the tradeoff between thermodynamic cost and precision in a sequence of events related to some internal changes of an otherwise hidden physical system. The precision is quantified by the fluctuations in either the number of events counted over time or the waiting times between successive events. Our results are valid for the same broad class of nonequilibrium driven systems considered by the thermodynamic uncertainty relation, but they extend to both time-symmetric and asymmetric observables. We show how optimal precision saturating the bounds can be achieved. For waiting-time fluctuations of asymmetric observables, a phase transition in the optimal configuration arises, where higher precision can be achieved by combining several signals.
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2
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Ertel B, Seifert U. Estimator of entropy production for partially accessible Markov networks based on the observation of blurred transitions. Phys Rev E 2024; 109:054109. [PMID: 38907510 DOI: 10.1103/physreve.109.054109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 03/25/2024] [Indexed: 06/24/2024]
Abstract
A central task in stochastic thermodynamics is the estimation of entropy production for partially accessible Markov networks. We establish an effective transition-based description for such networks with transitions that are not distinguishable and therefore blurred for an external observer. We demonstrate that, in contrast to a description based on fully resolved transitions, this effective description is typically non-Markovian at any point in time. Starting from an information-theoretic bound, we derive an operationally accessible entropy estimator for this observation scenario. We illustrate the operational relevance and the quality of this entropy estimator with a numerical analysis of various representative examples.
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Affiliation(s)
- Benjamin Ertel
- 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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3
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Blom K, Song K, Vouga E, Godec A, Makarov DE. Milestoning estimators of dissipation in systems observed at a coarse resolution. Proc Natl Acad Sci U S A 2024; 121:e2318333121. [PMID: 38625949 PMCID: PMC11047069 DOI: 10.1073/pnas.2318333121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 03/14/2024] [Indexed: 04/18/2024] Open
Abstract
Many nonequilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases, the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may-via a process called milestoning-improve entropy-production estimates. We present diverse examples where milestoning systematically renders observations "closer to underlying microscopic dynamics" and thereby improves thermodynamic inference from lumped data assuming a given range of memory, and we hypothesize that this effect is quite general. Moreover, whereas the correct general physical definition of time reversal in the presence of memory remains unknown, we here show by means of physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time reversal generally must be discarded.
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Affiliation(s)
- Kristian Blom
- Mathematical biophysics Group, Max Planck Institute for Multidisciplinary Sciences, Göttingen37077, Germany
| | - Kevin Song
- Department of Computer Science, University of Texas at Austin, Austin, TX78712
| | - Etienne Vouga
- Department of Computer Science, University of Texas at Austin, Austin, TX78712
| | - Aljaž Godec
- Mathematical biophysics Group, Max Planck Institute for Multidisciplinary Sciences, Göttingen37077, Germany
| | - Dmitrii E. Makarov
- Department of Chemistry and Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX78712
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4
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Zhao X, Hartich D, Godec A. Emergence of Memory in Equilibrium versus Nonequilibrium Systems. PHYSICAL REVIEW LETTERS 2024; 132:147101. [PMID: 38640391 DOI: 10.1103/physrevlett.132.147101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2023] [Accepted: 02/01/2024] [Indexed: 04/21/2024]
Abstract
Experiments often probe observables that correspond to low-dimensional projections of high-dimensional dynamics. In such situations distinct microscopic configurations become lumped into the same observable state. It is well known that correlations between the observable and the hidden degrees of freedom give rise to memory effects. However, how and under which conditions these correlations emerge remain poorly understood. Here we shed light on two fundamentally different scenarios of the emergence of memory in minimal stationary systems, where observed and hidden degrees of freedom either evolve cooperatively or are coupled by a hidden nonequilibrium current. In the reversible setting the strongest memory manifests when the timescales of hidden and observed dynamics overlap, whereas, strikingly, in the driven setting maximal memory emerges under a clear timescale separation. Our results hint at the possibility of fundamental differences in the way memory emerges in equilibrium versus driven systems that may be utilized as a "diagnostic" of the underlying hidden transport mechanism.
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Affiliation(s)
- Xizhu Zhao
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen
- Max Planck School Matter to Life, Jahnstraße 29, D-69120 Heidelberg, Germany
| | - David Hartich
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen
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5
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Di Terlizzi I, Gironella M, Herraez-Aguilar D, Betz T, Monroy F, Baiesi M, Ritort F. Variance sum rule for entropy production. Science 2024; 383:971-976. [PMID: 38422150 DOI: 10.1126/science.adh1823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 01/09/2024] [Indexed: 03/02/2024]
Abstract
Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.
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Affiliation(s)
- I Di Terlizzi
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - M Gironella
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Department of Medical Biochemistry and Cell Biology, Institute of Biomedicine, The Sahlgrenska Academy, University of Gothenburg, 40530 Gothenburg, Sweden
| | - D Herraez-Aguilar
- Facultad de Ciencias Experimentales, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1,800, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - T Betz
- Third Institute of Physics, Georg August Universität Göttingen, Göttingen, Germany
- Cluster of Excellence "Multiscale Bioimaging: from Molecular Machines to Networks of Excitable Cells" (MBExC), University of Göttingen, Göttingen, Germany
| | - F Monroy
- Departamento de Química Física, Facultad de Química, Universidad Complutense, 28040 Madrid, Spain
- Translational Biophysics, Instituto de Investigación Sanitaria Hospital Doce de Octubre (IMAS12), Av. Andalucía, 28041 Madrid, Spain
| | - M Baiesi
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - F Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain
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6
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Amorim F, Wisely J, Buckley N, DiNardo C, Sadasivan D. Predicting the Mpemba effect using machine learning. Phys Rev E 2023; 108:024137. [PMID: 37723698 DOI: 10.1103/physreve.108.024137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2022] [Accepted: 08/01/2023] [Indexed: 09/20/2023]
Abstract
The Mpemba effect can be studied with Markovian dynamics in a nonequilibrium thermodynamics framework. The Markovian Mpemba effect can be observed in a variety of systems including the Ising model. We demonstrate that the Markovian Mpemba effect can be predicted in the Ising model with several machine learning methods: the decision tree algorithm, neural networks, linear regression, and nonlinear regression with the least absolute shrinkage and selection operator (LASSO) method. The positive and negative accuracy of these methods are compared. Additionally, we find that machine learning methods can be used to accurately extrapolate to data outside the range in which they were trained. Neural networks can even predict the existence of the Mpemba effect when they are trained only on data in which the Mpemba effect does not occur. This indicates that information about which coefficients result in the Mpemba effect is contained in coefficients where the results does not occur. Furthermore, neural networks can predict that the Mpemba effect does not occur for positive J, corresponding to the ferromagnetic Ising model even when they are only trained on negative J, corresponding to the antiferromagnetic Ising model. All of these results demonstrate that the Mpemba effect can be predicted in complex, computationally expensive systems, without explicit calculations of the eigenvectors.
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Affiliation(s)
| | - Joey Wisely
- Ave Maria University, Ave Maria, Florida 34142, USA
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7
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Teza G, Yaacoby R, Raz O. Relaxation Shortcuts through Boundary Coupling. PHYSICAL REVIEW LETTERS 2023; 131:017101. [PMID: 37478423 DOI: 10.1103/physrevlett.131.017101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Revised: 07/06/2022] [Accepted: 05/17/2023] [Indexed: 07/23/2023]
Abstract
When a hot system cools down faster than an equivalent cold one, it exhibits the Mpemba effect (ME). This counterintuitive phenomenon was observed in several systems including water, magnetic alloys, and polymers. In most experiments the system is coupled to the bath through its boundaries, but all theories so far assumed bulk coupling. Here we build a general framework to characterize anomalous relaxations through boundary coupling, and present two emblematic setups: a diffusing particle and an Ising antiferromagnet. In the latter, we show that the ME can survive even arbitrarily weak couplings.
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Affiliation(s)
- Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Ran Yaacoby
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Oren Raz
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
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8
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van der Meer J, Degünther J, Seifert U. Time-Resolved Statistics of Snippets as General Framework for Model-Free Entropy Estimators. PHYSICAL REVIEW LETTERS 2023; 130:257101. [PMID: 37418719 DOI: 10.1103/physrevlett.130.257101] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Revised: 02/20/2023] [Accepted: 06/07/2023] [Indexed: 07/09/2023]
Abstract
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time reversal like a current. We introduce a general framework that allows us to infer a lower bound on entropy production through measuring the time-resolved statistics of events with any symmetry under time reversal, in particular, time-symmetric instantaneous events. We emphasize Markovianity as a property of certain events rather than of the full system and introduce an operationally accessible criterion for this weakened Markov property. Conceptually, the approach is based on snippets as particular sections of trajectories between two Markovian events, for which a generalized detailed balance relation is discussed.
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Affiliation(s)
- Jann van der Meer
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Julius Degünther
- 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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9
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Stella AL, Chechkin A, Teza G. Anomalous Dynamical Scaling Determines Universal Critical Singularities. PHYSICAL REVIEW LETTERS 2023; 130:207104. [PMID: 37267558 DOI: 10.1103/physrevlett.130.207104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Accepted: 04/19/2023] [Indexed: 06/04/2023]
Abstract
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at a large argument of the probability density function of rescaled displacement (scaling function) is derived and shown to imply universal singularities in the normalized cumulant generator. Exact calculations for continuous time random walks provide paradigmatic examples connected with singularities of second order phase transitions. In the biased case scaling is restricted to displacements in the drift direction and singularities have no equilibrium analogue.
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Affiliation(s)
- Attilio L Stella
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy and INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Aleksei Chechkin
- Institute of Physics and Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany, Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, University of Science and Technology, Wyspianskiego 27, 50-370 Wrocław, Poland, and Akhiezer Institute for Theoretical Physics National Science Center ''Kharkov Institute of Physics and Technology,'' 61108, Kharkiv, Ukraine
| | - Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
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10
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Teza G, Yaacoby R, Raz O. Eigenvalue Crossing as a Phase Transition in Relaxation Dynamics. PHYSICAL REVIEW LETTERS 2023; 130:207103. [PMID: 37267560 DOI: 10.1103/physrevlett.130.207103] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 04/07/2023] [Indexed: 06/04/2023]
Abstract
When a system's parameter is abruptly changed, a relaxation toward the new equilibrium of the system follows. We show that a crossing between the second and third eigenvalues of the relaxation operator results in a singularity in the dynamics analogous to a first-order equilibrium phase transition. While dynamical phase transitions are intrinsically hard to detect in nature, here we show how this kind of transition can be observed in an experimentally feasible four-state colloidal system. Finally, analytical proof of survival in the thermodynamic limit of a many body (1D Ising) model is provided.
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Affiliation(s)
- Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Ran Yaacoby
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Oren Raz
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
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11
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Stella AL, Chechkin A, Teza G. Universal singularities of anomalous diffusion in the Richardson class. Phys Rev E 2023; 107:054118. [PMID: 37329006 DOI: 10.1103/physreve.107.054118] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 04/21/2023] [Indexed: 06/18/2023]
Abstract
Inhomogeneous environments are rather ubiquitous in nature, often implying anomalies resulting in deviation from Gaussianity of diffusion processes. While sub- and superdiffusion are usually due to contrasting environmental features (hindering or favoring the motion, respectively), they are both observed in systems ranging from the micro- to the cosmological scale. Here we show how a model encompassing sub- and superdiffusion in an inhomogeneous environment exhibits a critical singularity in the normalized generator of the cumulants. The singularity originates directly and exclusively from the asymptotics of the non-Gaussian scaling function of displacement, and the independence from other details confers it a universal character. Our analysis, based on the method first applied by Stella et al. [Phys. Rev. Lett. 130, 207104 (2023)10.1103/PhysRevLett.130.207104], shows that the relation connecting the scaling function asymptotics to the diffusion exponent characteristic of processes in the Richardson class implies a nonstandard extensivity in time of the cumulant generator. Numerical tests fully confirm the results.
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Affiliation(s)
- Attilio L Stella
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy and INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Aleksei Chechkin
- Institute of Physics and Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany; Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, University of Science and Technology, Wyspianskiego 27, 50-370 Wrocław, Poland; and Akhiezer Institute for Theoretical Physics, National Science Center "Kharkov Institute of Physics and Technology", 61108 Kharkiv, Ukraine
| | - Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
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12
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Semaan MT, Crutchfield JP. First and second laws of information processing by nonequilibrium dynamical states. Phys Rev E 2023; 107:054132. [PMID: 37329111 DOI: 10.1103/physreve.107.054132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Accepted: 05/04/2023] [Indexed: 06/18/2023]
Abstract
The averaged steady-state surprisal links a driven stochastic system's information processing to its nonequilibrium thermodynamic response. By explicitly accounting for the effects of nonequilibrium steady states, a decomposition of the surprisal results in an information processing first law that extends and tightens-to strict equalities-various information processing second laws. Applying stochastic thermodynamics' integral fluctuation theorems then shows that the decomposition reduces to the second laws under appropriate limits. In unifying them, the first law paves the way to identifying the mechanisms by which nonequilibrium steady-state systems leverage information-bearing degrees of freedom to extract heat. To illustrate, we analyze an autonomous Maxwellian information ratchet that tunably violates detailed balance in its effective dynamics. This demonstrates how the presence of nonequilibrium steady states qualitatively alters an information engine's allowed functionality.
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Affiliation(s)
- Mikhael T Semaan
- Complexity Sciences Center and Department of Physics and Astronomy, University of California, Davis, One Shields Avenue, Davis, California 95616, USA
- Science Research Initiative, College of Science, University of Utah, Salt Lake City, Utah 84112, USA
| | - James P Crutchfield
- Complexity Sciences Center and Department of Physics and Astronomy, University of California, Davis, One Shields Avenue, Davis, California 95616, USA
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13
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Arbel-Goren R, McKeithen-Mead SA, Voglmaier D, Afremov I, Teza G, Grossman AD, Stavans J. Target search by an imported conjugative DNA element for a unique integration site along a bacterial chromosome during horizontal gene transfer. Nucleic Acids Res 2023; 51:3116-3129. [PMID: 36762480 PMCID: PMC10123120 DOI: 10.1093/nar/gkad068] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2022] [Revised: 01/18/2023] [Accepted: 01/25/2023] [Indexed: 02/11/2023] Open
Abstract
Integrative and conjugative elements (ICEs) are mobile genetic elements that can transfer by conjugation to recipient cells. Some ICEs integrate into a unique site in the genome of their hosts. We studied quantitatively the process by which an ICE searches for its unique integration site in the Bacillus subtilis chromosome. We followed the motion of both ICEBs1 and the chromosomal integration site in real time within individual cells. ICEBs1 exhibited a wide spectrum of dynamical behaviors, ranging from rapid sub-diffusive displacements crisscrossing the cell, to kinetically trapped states. The chromosomal integration site moved sub-diffusively and exhibited pronounced dynamical asymmetry between longitudinal and transversal motions, highlighting the role of chromosomal structure and the heterogeneity of the bacterial interior in the search. The successful search for and subsequent recombination into the integration site is a key step in the acquisition of integrating mobile genetic elements. Our findings provide new insights into intracellular transport processes involving large DNA molecules.
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Affiliation(s)
- Rinat Arbel-Goren
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | | | - Dominik Voglmaier
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Idana Afremov
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Alan D Grossman
- Department of Biology Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Joel Stavans
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
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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] [MESH Headings] [Grants] [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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Ertel B, van der Meer J, Seifert U. Operationally accessible uncertainty relations for thermodynamically consistent semi-Markov processes. Phys Rev E 2022; 105:044113. [PMID: 35590600 DOI: 10.1103/physreve.105.044113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2021] [Accepted: 03/21/2022] [Indexed: 06/15/2023]
Abstract
Semi-Markov processes generalize Markov processes by adding temporal memory effects as expressed by a semi-Markov kernel. We recall the path weight for a semi-Markov trajectory and the fact that thermodynamic consistency in equilibrium imposes a crucial condition called direction-time independence for which we present an alternative derivation. We prove a thermodynamic uncertainty relation that formally resembles the one for a discrete-time Markov process. The result relates the entropy production of the semi-Markov process to mean and variance of steady-state currents. We prove a further thermodynamic uncertainty relation valid for semi-Markov descriptions of coarse-grained Markov processes that emerge by grouping states together. A violation of this inequality can be used as an inference tool to conclude that a given semi-Markov process cannot result from coarse graining an underlying Markov one. We illustrate these results with representative examples.
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Affiliation(s)
- Benjamin Ertel
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Jann van der Meer
- 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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16
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Cocconi L, Salbreux G, Pruessner G. Scaling of entropy production under coarse graining in active disordered media. Phys Rev E 2022; 105:L042601. [PMID: 35590651 DOI: 10.1103/physreve.105.l042601] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Accepted: 03/11/2022] [Indexed: 01/01/2023]
Abstract
Entropy production plays a fundamental role in the study of nonequilibrium systems by offering a quantitative handle on the degree of time-reversal symmetry breaking. It depends crucially on the degree of freedom considered as well as on the scale of description. How the entropy production at one resolution of the degrees of freedom is related to the entropy production at another resolution is a fundamental question which has recently attracted interest. This relationship is of particular relevance to coarse-grained and continuum descriptions of a given phenomenon. In this work, we derive the scaling of the entropy production under iterative coarse graining on the basis of the correlations of the underlying microscopic transition rates for noninteracting particles in active disordered media. Our approach unveils a natural criterion to distinguish equilibrium-like and genuinely nonequilibrium macroscopic phenomena based on the sign of the scaling exponent of the entropy production per mesostate.
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Affiliation(s)
- Luca Cocconi
- Department of Mathematics, Imperial College, SW7 2BX London, United Kingdom.,Department of Genetics and Evolution, University of Geneva, Geneva, Switzerland.,The Francis Crick Institute, NW1 1AT London, United Kingdom
| | - Guillaume Salbreux
- Department of Genetics and Evolution, University of Geneva, Geneva, Switzerland
| | - Gunnar Pruessner
- Department of Mathematics, Imperial College, SW7 2BX London, United Kingdom
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17
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Speck T. Modeling of biomolecular machines in non-equilibrium steady states. J Chem Phys 2021; 155:230901. [PMID: 34937348 DOI: 10.1063/5.0070922] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling-even if often this step is not made explicit-and any model has to neglect details while still being physically accurate. Equilibrium statistical mechanics guides both the development of models and numerical methods for dynamics obeying detailed balance. For systems driven away from thermal equilibrium, such a universal theoretical framework is missing. For a restricted class of driven systems governed by Markov dynamics and local detailed balance, stochastic thermodynamics has evolved to fill this gap and to provide fundamental constraints and guiding principles. The next step is to advance stochastic thermodynamics from simple model systems to complex systems with tens of thousands or even millions of degrees of freedom. Biomolecules operating in the presence of chemical gradients and mechanical forces are a prime example for this challenge. In this Perspective, we give an introduction to isothermal stochastic thermodynamics geared toward the systematic multiscale modeling of the conformational dynamics of biomolecular and synthetic machines, and we outline some of the open challenges.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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18
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Skinner DJ, Dunkel J. Estimating Entropy Production from Waiting Time Distributions. PHYSICAL REVIEW LETTERS 2021; 127:198101. [PMID: 34797138 DOI: 10.1103/physrevlett.127.198101] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2021] [Accepted: 08/17/2021] [Indexed: 06/13/2023]
Abstract
Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication, or locomotion. Given time series observations of intra-, inter-, or multicellular processes, a key challenge is to detect nonequilibrium behavior and quantify the rate of free energy consumption. Obtaining reliable bounds on energy consumption and entropy production directly from experimental data remains difficult in practice, as many degrees of freedom typically are hidden to the observer, so that the accessible coarse-grained dynamics may not obviously violate detailed balance. Here, we introduce a novel method for bounding the entropy production of physical and living systems which uses only the waiting time statistics of hidden Markov processes and, hence, can be directly applied to experimental data. By determining a universal limiting curve, we infer entropy production bounds from experimental data for gene regulatory networks, mammalian behavioral dynamics, and numerous other biological processes. Further considering the asymptotic limit of increasingly precise biological timers, we estimate the necessary entropic cost of heartbeat regulation in humans, dogs, and mice.
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Affiliation(s)
- Dominic J Skinner
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
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19
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Bilotto P, Caprini L, Vulpiani A. Excess and loss of entropy production for different levels of coarse graining. Phys Rev E 2021; 104:024140. [PMID: 34525579 DOI: 10.1103/physreve.104.024140] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2021] [Accepted: 08/10/2021] [Indexed: 06/13/2023]
Abstract
We investigate the effect of coarse graining on the thermodynamic properties of a system, focusing on entropy production. As a case of study, we consider a one-dimensional colloidal particle in contact with a thermal bath, moving in a sinusoidal potential and driven out of equilibrium by a small constant force. Different levels of coarse graining are evaluated: At first, we compare the results in the underdamped dynamics with those in the overdamped one (first coarse graining). For large values of the friction coefficient, the two dynamics have the same thermodynamics properties, while, for smaller friction values, the overdamped approximation produces an excess of entropy production with respect to that of the underdamped dynamics. Moreover, for further smaller values of the drag coefficient, the excess of entropy production turns into a loss. These regimes are explained by evaluating the jump statistics, observing that the inertia is able to induce multiple jumps and affect the average jump rate. The periodic shape of the potential allows us to approximate the continuous dynamics via a Markov chain after the introduction of a suitable time and space discretization (second level of coarse graining). This discretization procedure is implemented starting both from the underdamped and the overdamped evolution and is analyzed for different values of the friction coefficient.
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Affiliation(s)
- Pierpaolo Bilotto
- Dipartimento di Fisica, Universitá di Roma Sapienza, 00185 Rome, Italy
| | - Lorenzo Caprini
- Scuola di Scienze e Tecnologie, Universitá di Camerino, 62032 Camerino, Italy
| | - Angelo Vulpiani
- Dipartimento di Fisica, Universitá di Roma Sapienza, 00185 Rome, Italy
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20
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Falasco G, Esposito M. Local detailed balance across scales: From diffusions to jump processes and beyond. Phys Rev E 2021; 103:042114. [PMID: 34005954 DOI: 10.1103/physreve.103.042114] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Accepted: 03/03/2021] [Indexed: 11/07/2022]
Abstract
Diffusive dynamics in presence of deep energy minima and weak nongradient forces can be coarse grained into a mesoscopic jump process over the various basins of attraction. Combining standard weak-noise results with a path integral expansion around equilibrium, we show that the emerging transition rates satisfy local detailed balance (LDB). Namely, the log ratio of the transition rates between nearby basins of attractions equals the free-energy variation appearing at equilibrium, supplemented by the work done by the nonconservative forces along the typical transition path. When the mesoscopic dynamics possesses a large-size deterministic limit, it can be further reduced to a jump process over macroscopic states satisfying LDB. The persistence of LDB under coarse graining of weakly nonequilibrium states is a generic consequence of the fact that only dissipative effects matter close to equilibrium.
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Affiliation(s)
- Gianmaria Falasco
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg
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21
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Yang X, Chen Y, Zhou T, Zhang J. Exploring dissipative sources of non-Markovian biochemical reaction systems. Phys Rev E 2021; 103:052411. [PMID: 34134237 DOI: 10.1103/physreve.103.052411] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 04/29/2021] [Indexed: 11/07/2022]
Abstract
Many biological processes including important intracellular processes are governed by biochemical reaction networks. Usually, these reaction systems operate far from thermodynamic equilibrium, implying free-energy dissipation. On the other hand, single reaction events happen often in a memory manner, leading to non-Markovian kinetics. A question then arises: how do we calculate free-energy dissipation (defined as the entropy production rate) in this physically real case? We derive an analytical formula for calculating the energy consumption of a general reaction system with molecular memory characterized by nonexponential waiting-time distributions. It shows that this dissipation is composed of two parts: one from broken detailed balance of an equivalent Markovian system with the same topology and substrates, and the other from the direction-time dependence of waiting-time distributions. But, if the system is in a detailed balance and the waiting-time distribution is direction-time independent, there is no energy dissipation even in the non-Markovian case. These general results provide insights into the physical mechanisms underlying nonequilibrium processes. A continuous-time random-walk model and a generalized model of stochastic gene expression are chosen to clearly show dissipative sources and the relationship between energy dissipation and molecular memory.
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Affiliation(s)
- Xiyan Yang
- School of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou 510521, People's Republic of China
| | - Yiren Chen
- College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, People's Republic of China
| | - Tianshou Zhou
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, People's Republic of China.,Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, People's Republic of China
| | - Jiajun Zhang
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, People's Republic of China.,Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, People's Republic of China
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22
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Teza G, Caraglio M, Stella AL. Entropic measure unveils country competitiveness and product specialization in the World trade web. Sci Rep 2021; 11:10189. [PMID: 33986366 PMCID: PMC8119984 DOI: 10.1038/s41598-021-89519-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Accepted: 04/21/2021] [Indexed: 12/29/2022] Open
Abstract
We show how the Shannon entropy function can be used as a basis to set up complexity measures weighting the economic efficiency of countries and the specialization of products beyond bare diversification. This entropy function guarantees the existence of a fixed point which is rapidly reached by an iterative scheme converging to our self-consistent measures. Our approach naturally allows to decompose into inter-sectorial and intra-sectorial contributions the country competitivity measure if products are partitioned into larger categories. Besides outlining the technical features and advantages of the method, we describe a wide range of results arising from the analysis of the obtained rankings and we benchmark these observations against those established with other economical parameters. These comparisons allow to partition countries and products into various main typologies, with well-revealed characterizing features. Our methods have wide applicability to general problems of ranking in bipartite networks.
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Affiliation(s)
- Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, 7610001, Rehovot, Israel
| | - Michele Caraglio
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, 6020, Innsbruck, Austria
| | - Attilio L Stella
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131, Padua, Italy. .,Sezione INFN Università di Padova, Via Marzolo 8, 35131, Padua, Italy.
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