Thermodynamics of driven systems with explicitly broken detailed balance

TL;DR

This paper develops a thermodynamic framework for driven systems with broken detailed balance, enabling the calculation of entropy and free energy in non-equilibrium steady states, thus extending thermodynamic concepts beyond equilibrium.

Contribution

It introduces a method to compute thermodynamic potentials in systems with broken detailed balance, clarifying their interpretation in non-equilibrium steady states.

Findings

Thermodynamic relations are established for driven, non-equilibrium processes.

Effective thermodynamic potentials can be unambiguously defined despite broken detailed balance.

The framework applies to sample space-reducing processes with steady states.

Abstract

In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose a challenge for a consistent thermodynamic interpretation. Even steady-state potentials like entropy or free energy are no longer state variables. Here, we use a framework for systems with broken detailed balance, where Boltzmann entropy can be computed while properly taking constraints on state transitions into account. As an illustration, we establish the thermodynamic relations for arbitrarily driven sample space-reducing processes that are non-equilibrium but show steady states. We demonstrate that, despite explicitly broken detailed balance, it remains feasible to define and unambiguously interpret the effective thermodynamic potentials.