Nonequilibrium fluctuations in a harmonic trap with annealed stochastic stiffness

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.