Nonequilibrium steady state thermodynamics and fluctuations for stochastic systems

TL;DR

This paper develops a thermodynamic framework for nonequilibrium steady states using a generalized Onsager-Machlup theory, revealing ambiguities in defining work and heat and illustrating how unique laws depend on system-specific physical arguments.

Contribution

It introduces a generalized Onsager-Machlup theory for nonequilibrium steady states and discusses ambiguities in defining thermodynamic quantities, proposing system-specific resolutions.

Findings

Multiple versions of thermodynamic laws exist for nonequilibrium steady states.

Ambiguities arise from non-uniqueness in time-reversal and heat separation.

Physical arguments are necessary to define unique thermodynamic relations.

Abstract

We use the work done on and the heat removed from a system to maintain it in a nonequilibrium steady state for a thermodynamic-like description of such a system as well as of its fluctuations. Based on a generalized Onsager-Machlup theory for nonequilibrium steady states we indicate two ambiguities, not present in an equilibrium state, in defining such work and heat: one due to a non-uniqueness of time-reversal procedures and another due to multiple possibilities to separate heat into work and an energy difference in nonequilibrium steady states. As a consequence, for such systems, the work and heat satisfy multiple versions of the first and second laws of thermodynamics as well as of their fluctuation theorems. Unique laws and relations appear only to be obtainable for concretely defined systems, using physical arguments to choose the relevant physical quantities. This is illustrated on a number of systems, including a Brownian particle in an electric field, a driven torsion pendulum, electric circuits and an energy transfer driven by a temperature difference.