Free energy and entropy production rate for a Brownian particle that walks on overdamped medium

TL;DR

This paper derives expressions for free energy and entropy rates of a Brownian particle in a viscous medium, analyzing their behavior out of equilibrium and at long times, including fluctuation theorem considerations.

Contribution

It provides a comprehensive theoretical framework for entropy and free energy dynamics of Brownian particles, including out-of-equilibrium conditions and fluctuation theorem analysis.

Findings

Entropy production and extraction rates decrease over time and saturate.

At long times, entropy production balances entropy extraction.

At equilibrium, both rates become zero.

Abstract

We derive general expressions for the free energy, entropy production and entropy extraction rates for a Brownian particle that walks in a viscous medium where the dynamics of its motion is governed by the Langevin equation. It is shown that when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In long time limit, the rate of entropy production balances the rate of entropy extraction and at equilibrium both entropy production and extraction rates become zero. Moreover, considering different model systems, not only we investigate how various thermodynamic quantities behave in time but also we discuss the fluctuation theorem in detail.