The generalized Kramers' theory for nonequilibrium open one-dimensional systems

TL;DR

This paper extends Kramers' theory to nonequilibrium open one-dimensional systems, accounting for both internal and external noise with arbitrary correlations, and derives a generalized rate expression applicable to various steady states.

Contribution

It introduces a generalized Kramers' rate formula for nonequilibrium open systems with stationary Gaussian noise, bridging closed and open system cases.

Findings

Derived a unified rate expression for nonequilibrium open systems.

Showed the generalized rate reduces to known cases for thermal and non-thermal steady states.

Highlighted the importance of nonequilibrium stationary distributions in activation processes.

Abstract

The Kramers' theory of activated processes is generalized for nonequilibrium open one-dimensional systems. We consider both the internal noise due to thermal bath and the external noise which are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. We stress the role of a nonequilibrium stationary state distribution for this open system which is reminiscent of an equilibrium Boltzmann distribution in calculation of rate. The generalized rate expression we derive here reduces to the specific limiting cases pertaining to the closed and open systems for thermal and non-thermal steady state activation processes.