Nonequilibrium steady states in Langevin thermal systems

TL;DR

This paper investigates the fundamental properties of steady states in Langevin thermal systems, revealing their equivalence in equilibrium and mutual exclusivity in nonequilibrium when velocity-dependent forces are involved.

Contribution

It demonstrates the equivalence of detailed balance, fluctuation-dissipation, and no heat dissipation in equilibrium Langevin systems, and shows their mutual exclusion in nonequilibrium systems with velocity-dependent forces.

Findings

In equilibrium, the three properties are equivalent.

In systems with velocity-dependent forces, the properties mutually exclude each other.

Steady states can retain some equilibrium properties without all of them.

Abstract

Equilibrium is characterized by its fundamental properties such as the detailed balance, the fluctuation-dissipation relation, and no heat dissipation. Based on the stochastic thermodynamics, we show that these three properties are equivalent to each other in conventional Langevin thermal systems with microscopic reversibility. Thus, a conventional steady state has either all three properties (equilibrium) or none of them (nonequilibrium). In contrast, with velocity-dependent forces breaking the microscopic reversibility, we prove that the detailed balance and the fluctuation-dissipation relation mutually exclude each other and no equivalence relation is possible between any two of the three properties. This implies that a steady state of Langevin systems with velocity-dependent forces may maintain some equilibrium properties but not all of them. Our results are illustrated with a few example systems.