Energy dissipation and violation of the fluctuation-response relation in non-equilibrium Langevin systems

TL;DR

This paper explores the violation of the fluctuation-response relation in non-equilibrium Langevin systems and relates it to energy dissipation, providing a comprehensive theoretical framework for various models.

Contribution

It offers a detailed derivation of the energy dissipation-fluctuation relation for diverse Langevin models, extending previous results.

Findings

The fluctuation-response violation correlates with energy dissipation.

The relation applies to many-body, Brownian, and time-dependent systems.

It enables experimental determination of energy dissipation rates.

Abstract

The fluctuation-response relation is a fundamental relation that is applicable to systems near equilibrium. On the other hand, when a system is driven far from equilibrium, this relation is violated in general because the detailed-balance condition is not satisfied in nonequilibrium systems. Even in this case, it has been found that for a class of Langevin equations, there exists an equality between the extent of violation of the fluctuation-response relation in the nonequilibrium steady state and the rate of energy dissipation from the system into the environment [T. Harada and S. -i. Sasa, Phys. Rev. Lett. 95, 130602 (2005)]. Since this equality involves only experimentally measurable quantities, it serves as a proposition to determine experimentally whether the system can be described by a Langevin equation. Furthermore, the contribution of each degree of freedom to the rate of energy dissipation can be determined based on this equality. In this paper, we present a comprehensive description on this equality, and provide a detailed derivation for various types of models including many-body systems, Brownian motor models, time-dependent systems, and systems with multiple heat reservoirs.