Nonequilibrium fluctuations in a harmonic trap with annealed stochastic stiffness

TL;DR

This paper analyzes the nonequilibrium fluctuations of an overdamped Brownian particle in a harmonic trap with a stochastically fluctuating stiffness modeled by an Ornstein-Uhlenbeck process, providing exact analytical results and numerical validation.

Contribution

It introduces a comprehensive analytical framework for the positional dynamics and thermodynamics of particles in traps with annealed stochastic stiffness, covering various correlation regimes.

Findings

Exact positional distribution and moments derived for different correlation times.

Analytical expressions for work and heat reveal nonequilibrium behavior.

Numerical simulations confirm analytical predictions.

Abstract

We provide a comprehensive analysis of the positional dynamics and average thermodynamics of an overdamped Brownian particle subject to both, harmonic confinement and annealed disorder due to a temporarily fluctuating trap stiffness. We model this stiffness via a stationary Ornstein-Uhlenbeck (OU) process whose correlation time can be tuned from white noise to a quenched limit. We analytically calculate the positional distribution in these limits and provide exact expressions for the $n$th positional moments at finite correlation times, revealing important insights regarding stationarity. Further, we analyze the average work performed on the particle and the heat dissipated into the environment at all times, illustrating the nonequilibrium character of the system and its relaxation into a steady state. Our analytical results are validated by numerical Langevin simulations.