Stochastic theory of nonequilibrium steady states and its applications. Part I

Zhang, Xuejuan; Qian, Hong; Qian, Min

doi:10.1016/j.physrep.2011.09.002

Cited by 171 publications

(191 citation statements)

References 173 publications

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“…In this paper, we present a brief introduction to stochastic thermodynamics. We refer to the literature for more advanced reviews [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Ensemble and trajectory thermodynamics: A brief introduction

Broeck

Esposito

2015

Physica A: Statistical Mechanics and its Applications

335

435

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h i g h l i g h t s• We review stochastic thermodynamics at the ensemble level.• We formulate first and second laws at the trajectory level.• The stochastic entropy production is the log-ratio of trajectory probabilities.• We establish the relation between the stochastic grand potential, work and entropy production.• We derive detailed and integral fluctuation theorems. a r t i c l e i n f o b s t r a c tWe revisit stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir.

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“…In this paper, we present a brief introduction to stochastic thermodynamics. We refer to the literature for more advanced reviews [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Ensemble and trajectory thermodynamics: A brief introduction

Broeck

Esposito

2015

Physica A: Statistical Mechanics and its Applications

335

435

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“…Adiabatic and nonadiabatic nonequilibrium dynamics has been studied computationally or theoretically on gene switches (9-21) and molecular motors (22)(23)(24). However, a global description and framework of understanding is still challenging and in demand.…”

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confidence: 99%

Eddy current and coupled landscapes for nonadiabatic and nonequilibrium complex system dynamics

Zhang

Sasai

Wang

2013

Proc. Natl. Acad. Sci. U.S.A.

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Physical and biological systems are often involved with coupled processes of different time scales. In the system with electronic and atomic motions, for example, the interplay between the atomic motion along the same energy landscape and the electronic hopping between different landscapes is critical: the system behavior largely depends on whether the intralandscape motion is slower (adiabatic) or faster (nonadiabatic) than the interlandscape hopping. For general nonequilibrium dynamics where Hamiltonian or energy function is unknown a priori, the challenge is how to extend the concepts of the intra-and interlandscape dynamics. In this paper we establish a theoretical framework for describing global nonequilibrium and nonadiabatic complex system dynamics by transforming the coupled landscapes into a single landscape but with additional dimensions. On this single landscape, dynamics is driven by gradient of the potential landscape, which is closely related to the steadystate probability distribution of the enlarged dimensions, and the probability flux, which has a curl nature. Through an example of a self-regulating gene circuit, we show that the curl flux has dramatic effects on gene regulatory dynamics. The curl flux and landscape framework developed here are easy to visualize and can be used to guide further investigation of physical and biological nonequilibrium systems.nonequilibrium landscape | adiabaticity | nonadiabaticity H eterogeneity among coupled processes is a hallmark of complex behaviors of physical and biological systems. A photoexcited molecule, for example, may relax into different low-energy states depending on the difference among time scales of electronic and atomic motions. Molecular motors are fueled by ATP hydrolysis and move into the different structural states, where the heterogeneous distribution of time scales of reactions and structural changes should characterize the motor performance. Dynamical complexity owing to the interplay of heterogeneous processes with multiple time scales can give rise to rich phenomena.In a system having multiple time scales, some dynamical quantities may take discrete values whereas others are continuous. An example of such heterogeneity is found in the electron-transfer reaction, in which the electronic state is discrete and atomic motions are continuous (1). Then, the system can be represented by multiple electronic energy surfaces and the change in atomic positions is motion along individual surfaces. Complex behaviors of the system are explained by the combined process of intrasurface motion along the same and intersurface hopping between different electronic energy surface(s). If the intrasurface motion is slower (faster) than the intersurface hopping, the process is called adiabatic (nonadiabatic). We here extend this notion, the significance of adiabatic and nonadiabatic effects, beyond the Hamiltonian systems to general nonequilibrium problems. Indeed, important complex systems such as reaction networks, gene switches, and molecular motors are co...

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“…The first is based on a potential energy landscape perspective (Ao, 2004;Ao et al, 2007;Han and Wang, 2007;Kim and Wang, 2007;Lapidus et al, 2008;Wang et al, 2010aWang et al, , 2008Wang et al, , 2010bWang et al, ,c, 2011Zhou and Qian, 2011) and leads to a powerful approach for conceptualizing and quantifying emergent complex behavior in nonlinear biochemical reaction networks with stochastic dynamics. The second methodology is based on nonequilibrium stochastic thermodynamics Gaspard, 2004, 2007;van den Broeck and Esposito, 2010;Demirel, 2010;Esposito and van den Broeck, 2010b;Ge, 2009;Ge and Qian, 2010;Ge et al, 2012;Han and Wang, 2008;Jiang et al, 2004;Luo et al, 2002;Mou et al, 1986;Puglisi et al, 2010;Qian, 2006Qian, , 2009Qian, , 2010Rao et al, 2011;Ross, 2008;Ross and Villaverde, 2010;Santillán and Qian, 2011;Schlögl, 1980;Schmiedl and Seifert, 2007;Schnakenberg, 1976;Seifert, 2008;Vellela and Qian, 2009;Zhang et al, 2012) and can be effectively used to study the macroscopic behavior of Markovian biochemical reaction networks and, in particular, properties related to their self-organization, functional stability, robustness and evolutionary behavior (Haken, 1975;Han and Wang, ...…”

Section: Introductionmentioning

confidence: 99%

Markovian dynamics on complex reaction networks

2013

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Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underling population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions, the computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples.

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Stochastic theory of nonequilibrium steady states and its applications. Part I

Cited by 171 publications

References 173 publications

Ensemble and trajectory thermodynamics: A brief introduction

Ensemble and trajectory thermodynamics: A brief introduction

Eddy current and coupled landscapes for nonadiabatic and nonequilibrium complex system dynamics

Markovian dynamics on complex reaction networks

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