On and beyond entropy production: the case of Markov jump processes

TL;DR

This paper explores how entropy production characterizes near-equilibrium states in Markov jump processes and introduces a broader framework involving time-symmetric dynamical activity for far-from-equilibrium fluctuations.

Contribution

It extends fluctuation theory by incorporating time-symmetric dynamical activity, providing an extended Onsager-Machlup Lagrangian applicable to nonequilibrium systems.

Findings

Entropy derivatives characterize near-equilibrium states.

Time-symmetric dynamical activity becomes crucial far from equilibrium.

Extended Onsager-Machlup Lagrangian describes small fluctuations.

Abstract

How is it that entropy derivatives almost in their own are characterizing the state of a system close to equilibrium, and what happens further away from it? We explain within the framework of Markov jump processes why fluctuation theory can be based on considerations involving entropy production alone when perturbing around the detailed balance condition. Variational principles such as that of minimum entropy production are understood in that way. Yet, further away from equilibrium, dynamical fluctuations reveal a structure where the time-symmetric sector crucially enters. The fluctuations of densities and currents get coupled and a time-symmetric notion of dynamical activity becomes the counterpart and equal player to the entropy production. The results are summarized in an extended Onsager-Machlup Lagrangian, which in its quadratic approximation is expected to be quite general in governing the small fluctuations of nonequilibrium systems whose macroscopic behavior can be written in terms of a Master equation autonomously describing the time-dependence of densities and currents.