Potential and Flux Decomposition for Dynamical Systems and Non-Equilibrium Thermodynamics: Curvature, Gauge Field and Generalized Fluctuation-Dissipation Theorem

TL;DR

This paper develops a generalized fluctuation-dissipation theorem for non-equilibrium systems, linking potential flux decomposition, gauge fields, and thermodynamics, providing new insights into response functions and entropy production.

Contribution

It introduces a generalized FDT incorporating curl flux and gauge curvature, extending near-equilibrium concepts to non-equilibrium thermodynamics.

Findings

Decomposition of response into spontaneous and flux-related parts

Connection between fluctuation theorem and generalized FDT

Entropy production split into relaxation and housekeeping contributions

Abstract

The driving force of the dynamical system can be decomposed into the gradient of a potential landscape and curl flux (current). The fluctuation-dissipation theorem (FDT) is often applied to near equilibrium systems with detailed balance. The response due to a small perturbation can be expressed by a spontaneous fluctuation. For non-equilibrium systems, we derived a generalized FDT that the response function is composed of two parts: (1) a spontaneous correlation representing the relaxation which is present in the near equilibrium systems with detailed balance; (2) a correlation related to the persistence of the curl flux in steady state, which is also in part linked to a internal curvature of a gauge field. The generalized FDT is also related to the fluctuation theorem. In the equal time limit, the generalized FDT naturally leads to non-equilibrium thermodynamics where the entropy production rate can be decomposed into spontaneous relaxation driven by gradient force and house keeping contribution driven by the non-zero flux that sustains the non-equilibrium environment and breaks the detailed balance.