Non-equilibrium thermodynamics for functionals of current and density

TL;DR

This paper develops a large-deviation framework for non-equilibrium steady states, deriving explicit functionals for current and density in stochastic many-body systems, and relates various thermodynamic quantities.

Contribution

It introduces the Current-Density Cramer Functional (CDCF) for irreversible Langevin dynamics and Markov chains, providing a new formalism for non-equilibrium fluctuations.

Findings

Explicit CDCF derived for Langevin and Markov systems

Relations between different linear functionals and CDCF established

Illustrative model example demonstrating the formalism

Abstract

We study a stochastic many-body system maintained in an non-equilibrium steady state. Probability distribution functional of the time-integrated current and density is shown to attain a large-deviation form in the long-time asymptotics. The corresponding Current-Density Cramer Functional (CDCF) is explicitly derived for irreversible Langevin dynamics and discrete-space Markov chains. We also show that the Cramer functionals of other linear functionals of density and current, like work generated by a force, are related to CDCF in a way reminiscent of variational relations between different thermodynamic potentials. The general formalism is illustrated with a model example.