Work Relations Connecting Nonequilibrium Steady States Without Detailed Balance

TL;DR

This paper develops a framework to define thermodynamic quantities in nonequilibrium steady states lacking detailed balance by constructing a potential function, extending classical thermodynamics and fluctuation theorems.

Contribution

It introduces a method to construct potential functions in nonequilibrium systems, generalizing equilibrium concepts and fluctuation theorems without requiring detailed balance.

Findings

Constructed potential functions for nonequilibrium steady states.

Derived exact work distributions for time-dependent systems.

Extended Jarzynski and Crooks fluctuation theorems to systems without detailed balance.

Abstract

Bridging equilibrium and nonequilibrium statistical physics attracts sustained interest. Hallmarks of nonequilibrium systems include a breakdown of detailed balance, and an absence of a priori potential function corresponding to the Boltzmann-Gibbs distribution, without which classical equilibrium thermodynamical quantities could not be defined. Here, we construct dynamically the potential function through decomposing the system into a dissipative part and a conservative part, and develop a nonequilibrium theory by defining thermodynamical quantities based on the potential function. Concepts for equilibrium can thus be naturally extended to nonequilibrium steady state. We elucidate this procedure explicitly in a class of time-dependent linear diffusive systems without mathematical ambiguity. We further obtain the exact work distribution for an arbitrary control parameter, and work equalities connecting nonequilibrium steady states. Our results provide a direct generalization on Jarzynski equality and Crooks fluctuation theorem to systems without detailed balance.