Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle

TL;DR

This paper provides an exact analytical solution for the nonequilibrium relaxation dynamics of a trapped nanoparticle, demonstrating the validity of the heat exchange fluctuation theorem far from equilibrium.

Contribution

It introduces a novel exact solution to Langevin dynamics for a nanoparticle in a harmonic trap, extending to multiple particles and validating fluctuation theorems.

Findings

Exact time-dependent solution for Langevin dynamics

Validation of heat exchange fluctuation theorem far from equilibrium

Analytical and numerical corroboration of results

Abstract

In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from the stochastic differential equation of our system's energy in the underdamped regime. By utilizing this stochastic thermodynamics approach, we are able to completely describe the heat exchange process between the nanoparticle and the surrounding environment. As an important consequence of our results, we observe the validity of the heat exchange fluctuation theorem (XFT) in our setup, which holds for systems arbitrarily far from equilibrium conditions. By extending our results for the case of $N$ noninterating nanoparticles, we perform analytical asymptotic limits and direct numerical simulations that corroborate our analytical predictions.