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

• Published in: Physics reports Vol. 510; no. 1; pp. 1 - 86
• Main Authors: Zhang, Xue-Juan, Qian, Hong, Qian, Min
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 2012; Elsevier
• Subjects: Brownian motor; Entropy production; Exact sciences and technology; Fluctuations; Irreversibility; Markov process; Molecular motor; Noise-induced phenomenon; Physics; Stochastic resonance; Markov process; Fluctuations; Noise-induced phenomenon; Stochastic resonance; Irreversibility; Molecular motor; Entropy production; Brownian motor; Discrete systems; Non equilibrium system; Nonlinear differential equations; Probability theory; Entropy; Fokker-Planck equation; Free energy; Production rate; Stochastic systems; Energy dissipation; Stochastic theory; Diffusion process; Stationary process; Master equations
• ISSN: 0370-1573; 1873-6270
• DOI: 10.1016/j.physrep.2011.09.002

The concepts of equilibrium and nonequilibrium steady states are introduced in the present review as mathematical concepts associated with stationary Markov processes. For both discrete stochastic systems with master equations and continuous diffusion processes with Fokker–Planck equations, the nonequilibrium steady state (NESS) is characterized in terms of several key notions which are originated from nonequilibrium physics: time irreversibility, breakdown of detailed balance, free energy dissipation, and positive entropy production rate. After presenting this NESS theory in pedagogically accessible mathematical terms that require only a minimal amount of prerequisites in nonlinear differential equations and the theory of probability, it is applied, in Part I, to two widely studied problems: the stochastic resonance (also known as coherent resonance) and molecular motors (also known as Brownian ratchet). Although both areas have advanced rapidly on their own with a vast amount of literature, the theory of NESS provides them with a unifying mathematical foundation. Part II of this review contains applications of the NESS theory to processes from cellular biochemistry, ranging from enzyme catalyzed reactions, kinetic proofreading, to zeroth-order ultrasensitivity.