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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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Xiang X, Zhou J, Deng Y, Yang X. Identifying the generator matrix of a stationary Markov chain using partially observable data. CHAOS (WOODBURY, N.Y.) 2024; 34:023132. [PMID: 38386908 DOI: 10.1063/5.0156458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2023] [Accepted: 01/23/2024] [Indexed: 02/24/2024]
Abstract
Given that most states in real-world systems are inaccessible, it is critical to study the inverse problem of an irreversibly stationary Markov chain regarding how a generator matrix can be identified using minimal observations. The hitting-time distribution of an irreversibly stationary Markov chain is first generalized from a reversible case. The hitting-time distribution is then decoded via the taboo rate, and the results show remarkably that under mild conditions, the generator matrix of a reversible Markov chain or a specific case of irreversibly stationary ones can be identified by utilizing observations from all leaves and two adjacent states in each cycle. Several algorithms are proposed for calculating the generator matrix accurately, and numerical examples are presented to confirm their validity and efficiency. An application to neurophysiology is provided to demonstrate the applicability of such statistics to real-world data. This means that partially observable data can be used to identify the generator matrix of a stationary Markov chain.
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Affiliation(s)
- Xuyan Xiang
- School of Mathematics and Physics Science, Hunan University of Arts and Science, Changde 415000, China
- College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
| | - Jieming Zhou
- College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
| | - Yingchun Deng
- College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
| | - Xiangqun Yang
- College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
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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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Schmid S, Hugel T. Efficient use of single molecule time traces to resolve kinetic rates, models and uncertainties. J Chem Phys 2018; 148:123312. [PMID: 29604821 DOI: 10.1063/1.5006604] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Single molecule time traces reveal the time evolution of unsynchronized kinetic systems. Especially single molecule Förster resonance energy transfer (smFRET) provides access to enzymatically important time scales, combined with molecular distance resolution and minimal interference with the sample. Yet the kinetic analysis of smFRET time traces is complicated by experimental shortcomings-such as photo-bleaching and noise. Here we recapitulate the fundamental limits of single molecule fluorescence that render the classic, dwell-time based kinetic analysis unsuitable. In contrast, our Single Molecule Analysis of Complex Kinetic Sequences (SMACKS) considers every data point and combines the information of many short traces in one global kinetic rate model. We demonstrate the potential of SMACKS by resolving the small kinetic effects caused by different ionic strengths in the chaperone protein Hsp90. These results show an unexpected interrelation between conformational dynamics and ATPase activity in Hsp90.
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Affiliation(s)
- Sonja Schmid
- Institute of Physical Chemistry II, University of Freiburg, Albertstr. 23 a, 79104 Freiburg, Germany
| | - Thorsten Hugel
- Institute of Physical Chemistry II, University of Freiburg, Albertstr. 23 a, 79104 Freiburg, Germany
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Yang SX, Ge H. Decomposition of the entropy production rate and nonequilibrium thermodynamics of switching diffusion processes. Phys Rev E 2018; 98:012418. [PMID: 30110804 DOI: 10.1103/physreve.98.012418] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2018] [Indexed: 12/15/2022]
Abstract
A switching diffusion process (SDP) is a widely used stochastic model in physics and biology, especially for molecular motors that exhibit a discrete internal chemical kinetics as well as a continuous external mechanical motion. The nonequilibrium thermodynamics of switching diffusion processes has not been extensively studied yet. In the present paper, we propose the decomposition of the entropy production rate in one-dimensional SDPs, based on the flux decomposition. However, similar decompositions of the housekeeping heat dissipation rate and free energy dissipation rate cannot guarantee the non-negativity of each decomposed component. Hence, we modify this decomposition with the flow of exponential relative information under steady-state fluxes, resulting in another decomposition with all non-negative components. Furthermore, we also provide the nonequilibrium thermodynamics of one-dimensional SDPs under the perspectives of coarse -graining and exchange of information between the chemical kinetics and mechanical motion, resulting in several other decompositions of entropy production rate. Finally, we generalize all the results to high-dimensional SDPs with a more general mathematical treatment.
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Affiliation(s)
- Shi-Xian Yang
- School of Mathematics and Statistics, Chongqing University, Chongqing 400044, China
| | - Hao Ge
- Beijing International Center for Mathematical Research (BICMR) and Biomedical Pioneering Innovation Center (BIOPIC), Peking University, Beijing 100871, China
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Single-Molecule Analysis beyond Dwell Times: Demonstration and Assessment in and out of Equilibrium. Biophys J 2017; 111:1375-1384. [PMID: 27705761 DOI: 10.1016/j.bpj.2016.08.023] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2016] [Revised: 08/01/2016] [Accepted: 08/09/2016] [Indexed: 11/21/2022] Open
Abstract
We present a simple and robust technique for extracting kinetic rate models and thermodynamic quantities from single-molecule time traces. Single-molecule analysis of complex kinetic sequences (SMACKS) is a maximum-likelihood approach that resolves all statistically relevant rates and also their uncertainties. This is achieved by optimizing one global kinetic model based on the complete data set while allowing for experimental variations between individual trajectories. In contrast to dwell-time analysis, which is the current standard method, SMACKS includes every experimental data point, not only dwell times. As a result, it works as well for long trajectories as for an equivalent set of short ones. In addition, the previous systematic overestimation of fast over slow rates is solved. We demonstrate the power of SMACKS on the kinetics of the multidomain protein Hsp90 measured by single-molecule Förster resonance energy transfer. Experiments in and out of equilibrium are analyzed and compared to simulations, shedding new light on the role of Hsp90's ATPase function. SMACKS resolves accurate rate models even if states cause indistinguishable signals. Thereby, it pushes the boundaries of single-molecule kinetics beyond those of current methods.
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Zimmermann E, Seifert U. Effective rates from thermodynamically consistent coarse-graining of models for molecular motors with probe particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022709. [PMID: 25768533 DOI: 10.1103/physreve.91.022709] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Indexed: 06/04/2023]
Abstract
Many single-molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it. The theoretical analysis of these assays, however, often takes into account only the degrees of freedom representing the motor. We present a coarse-graining method that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one-particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way. The coarse-grained rates obey a local detailed balance condition and reproduce the net currents. Moreover, the average entropy production as well as the thermodynamic efficiency is invariant under this coarse-graining procedure. Our analysis reveals that only by assuming unrealistically fast probe particles, the coarse-grained transition rates coincide with the transition rates of the traditionally used one-particle motor models. Additionally, we find that for multicyclic motors the stall force can depend on the probe size. We apply this coarse-graining method to specific case studies of the F(1)-ATPase and the kinesin motor.
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Affiliation(s)
- Eva Zimmermann
- 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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Muy S, Kundu A, Lacoste D. Non-invasive estimation of dissipation from non-equilibrium fluctuations in chemical reactions. J Chem Phys 2013; 139:124109. [DOI: 10.1063/1.4821760] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Seifert U. Stochastic thermodynamics, fluctuation theorems and molecular machines. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:126001. [PMID: 23168354 DOI: 10.1088/0034-4885/75/12/126001] [Citation(s) in RCA: 1175] [Impact Index Per Article: 97.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
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Affiliation(s)
- Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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Esposito M. Stochastic thermodynamics under coarse graining. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041125. [PMID: 22680437 DOI: 10.1103/physreve.85.041125] [Citation(s) in RCA: 125] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2011] [Indexed: 06/01/2023]
Abstract
A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of "mesostates" (e.g., sets of "microstates"), the consequence on the thermodynamic description of the system is studied in detail. When microstates within mesostates rapidly thermalize, the entire structure of the microscopic theory is recovered at the mesostate level. This is not the case when these microstates remain out of equilibrium, leading to additional contributions to the entropy balance. Some of our results are illustrated for a model of two coupled quantum dots.
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Affiliation(s)
- Massimiliano Esposito
- Complex Systems and Statistical Mechanics, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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Roldán E, Parrondo JMR. Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031129. [PMID: 22587060 DOI: 10.1103/physreve.85.031129] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2012] [Indexed: 05/31/2023]
Abstract
The irreversibility of a stationary time series can be quantified using the Kullback-Leibler divergence (KLD) between the probability of observing the series and the probability of observing the time-reversed series. Moreover, this KLD is a tool to estimate entropy production from stationary trajectories since it gives a lower bound to the entropy production of the physical process generating the series. In this paper we introduce analytical and numerical techniques to estimate the KLD between time series generated by several stochastic dynamics with a finite number of states. We examine the accuracy of our estimators for a specific example, a discrete flashing ratchet, and investigate how close the KLD is to the entropy production depending on the number of degrees of freedom of the system that are sampled in the trajectories.
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Affiliation(s)
- Edgar Roldán
- Departamento de Física Atómica, Molecular y Nuclear and GISC, Universidad Complutense de Madrid, 28040 Madrid, Spain
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Roldán E, Parrondo JMR. Estimating dissipation from single stationary trajectories. PHYSICAL REVIEW LETTERS 2010; 105:150607. [PMID: 21230886 DOI: 10.1103/physrevlett.105.150607] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2010] [Revised: 08/06/2010] [Indexed: 05/30/2023]
Abstract
In this Letter we show that the time reversal asymmetry of a stationary time series provides information about the entropy production of the physical mechanism generating the series, even if one ignores any detail of that mechanism. We develop estimators for the entropy production which can detect nonequilibrium processes even when there are no measurable flows in the time series.
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Affiliation(s)
- Edgar Roldán
- Departamento de Física Atómica, Molecular y Nuclear and GISC, Universidad Complutense de Madrid, 28040-Madrid, Spain
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