On the steady state probability distribution of nonequilibrium stochastic systems

TL;DR

This paper explores the relationship between driving forces and steady state probability distributions in nonequilibrium stochastic systems, introducing a force decomposition method to analyze different force fields compatible with a given steady state.

Contribution

It presents a force decomposition approach that helps understand the steady state distributions in nonequilibrium stochastic systems, applicable to both overdamped and underdamped dynamics.

Findings

Force decomposition reveals multiple compatible force fields for a given steady state.

The method applies to both overdamped and underdamped stochastic systems.

Insights into nonequilibrium steady state behavior are gained through the decomposition.

Abstract

A driven stochastic system in a constant temperature heat bath relaxes into a steady state which is characterized by the steady state probability distribution. We investigate the relationship between the driving force and the steady state probability distribution. We adopt the force decomposition method in which the force is decomposed as the sum of a gradient of a steady state potential and the remaining part. The decomposition method allows one to find a set of force fields each of which is compatible to a given steady state. Such a knowledge provides a useful insight on stochastic systems especially in the nonequilibrium situation. We demonstrate the decomposition method in stochastic systems under overdamped and underdamped dynamics and discuss the connection between them.