The generalized Kramers' theory for an external noise driven bath

TL;DR

This paper extends Kramers' theory to systems coupled with a reservoir influenced by external Gaussian noise, deriving a generalized escape rate for nonequilibrium conditions.

Contribution

It introduces a generalized Kramers' rate formula for systems with reservoirs driven by external noise, broadening the applicability of escape rate theory.

Findings

Derived a generalized Kramers' rate for external noise-driven reservoirs.

Established a relation between dissipation and response function in nonequilibrium systems.

Applicable to systems with arbitrary decaying correlation functions of noise.

Abstract

We consider a system-reservoir model where the reservoir is modulated by an external noise. Both the internal noise of the reservoir and the external noise are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. Based on a relation between the dissipation of the system and the response function of the reservoir driven by external noise we derive the generalized Kramers' rate for this nonequilibrium open system.