Non-equilibrium thermodynamics of diffusion in fluctuating potentials

TL;DR

This paper develops analytical methods to quantify entropy production in non-equilibrium diffusion processes influenced by fluctuating potentials, with applications to stochastic resetting, optical traps, and biological systems.

Contribution

It provides exact analytical results for entropy production in systems driven by arbitrary fluctuating potentials, extending non-equilibrium thermodynamics to complex stochastic environments.

Findings

Derived formulas for steady-state entropy production in fluctuating potentials.

Analyzed a harmonic trap with time-varying stiffness, including Markovian fluctuations.

Introduced an effective stochastic resetting model with finite entropy production.

Abstract

A positive rate of entropy production at steady state is a distinctive feature of truly non-equilibrium processes. Exact results, while being often limited to simple models, offer a unique opportunity to explore the thermodynamic features of these processes in full details. Here we derive analytical results for the steady-state rate of entropy production in single particle systems driven away from equilibrium by the fluctuations of an external potential of arbitrary shapes. Subsequently, we provide exact results for a diffusive particle in a harmonic trap whose potential stiffness varies in time according to both discrete and continuous Markov processes. In particular, studying the case of a fully intermittent potential allows us to introduce an effective model of stochastic resetting for which it is possible to obtain finite non-negative entropy production. Altogether, this work lays the foundation for a non-equilibrium thermodynamic theory of fluctuating potentials, with immediate applications to stochastic resetting processes, fluctuations in optical traps and fluctuating interactions in living systems.