Nonlinear Stochastic Dynamics of Complex Systems, II: Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality

Abstract

In this paper we revisit the notion of the "minus logarithm of stationary probability" as a generalized potential in nonequilibrium systems and attempt to illustrate its central role in an axiomatic approach to stochastic nonequilibrium thermodynamics of complex systems. It is demonstrated that this quantity arises naturally through both monotonicity results of Markov processes and as the rate function when a stochastic process approaches a deterministic limit. We then undertake a more detailed mathematical analysis of the consequences of this quantity, culminating in a necessary and sufficient condition for the criticality of stochastic systems. This condition is then discussed in the context of recent results about criticality in biological systems

arXiv comment28 pages

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Cited by in corpus (5)

• Unified formalism for entropy productions and fluctuation relations
• Mathematical Representation of Clausius' and Kelvin's Statements of the Second Law and Irreversibility
• Potentials of Continuous Markov Process and Random Perturbations
• Nonlinear Stochastic Dynamics of Complex Systems, I: A Chemical Reaction Kinetic Perspective with Mesoscopic Nonequilibrium Thermodynamics
• Nonlinear Stochastic Dynamics of Complex Systems, III: Noneqilibrium Thermodynamics of Self-Replication Kinetics