Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states

By Royce K. P. Zia, B. Schmittmann. 2007

199 citations recorded by the source corpus.

One of the key features of non-equilibrium steady states (NESS) is the presence of non-trivial probability currents. We propose a general classification of NESS in which these currents play a central distinguishing role. As a corollary, we specify the transformations of the dynamic transition rates which leave a given NESS invariant. The formalism is most transparent within a continuous-time master equation framework since it allows for a general graph-theoretical representation of the NESS. We discuss the consequences of these transformations for entropy production, present several simple examples, and explore some generalizations, to discrete time and continuous variables.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/15282d3d8ff71a954503c22c2836ee8ef77cea53

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

A pedestrian's view on interacting particle systems, KPZ universality and random matrices (2008, background): “where Kij is the net probability current between states i and j [144].”
Nonequilibrium physics in biology (2019, methodology): “Another method decomposed discrete Markov chains into two parts: one that preserved and another that broke detailed balance (Qian and Hou, 1979; Schnakenberg, 1976; Zhang and Wang, 2014; Zia and Schmittmann, 2007).”
Stochastic thermodynamics: From principles to the cost of precision (2017, background): “, in [14], which works particularly well for small networks.”
Stochastic thermodynamics, fluctuation theorems and molecular machines (2012, background): “In the latter case, there are non-vanishing steady state probability currents jsmn ≡ p s mwmn − p s nwnm = −j s nm. (114) Since knowing psn is not sufficient to distinguish a genuine equilibrium from a NESS, Zia and Schmittmann [191, 192] suggested to characterize a NESS by its stationary distributi”
Nonequilibrium steady states of matrix-product form: a solver's guide (2007, background): “in terms of statistical weights f(C), each of which is given by the determinant of the matrix of transition rates obtained by removing the row and column corresponding to the conﬁguration C (see e.g. [13,14]). To arrive at the probability distribution P(C) one requires the normalisation Z = P C f(C)”
Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport (2011, unknown): “Referring readers to a recent article [7] for the details, we provide brief 392 summaries here for a few key points.”