Periodically Driven Harmonic Langevin Systems

TL;DR

This paper analyzes the long-term behavior of periodically driven harmonic Langevin systems, providing nearly exact asymptotic distributions and exploring energy, entropy, and response dynamics using symmetry and nonperturbative methods.

Contribution

It offers a nonperturbative analysis of asymptotic states in periodically driven harmonic Langevin systems, including both overdamped and underdamped cases, using symmetry and advanced mathematical techniques.

Findings

Exact asymptotic distributions for driven harmonic systems

Analysis of energy and entropy fluctuations under periodic driving

Characterization of response functions to perturbations

Abstract

Motivated to understand the asymptotic behavior of periodically driven thermodynamic systems, we study the prototypical example of Brownian particle, overdamped and underdamped, in harmonic potentials subjected to periodic driving. The harmonic strength and the coefficients of drift and diffusion are all taken to be $T$-periodic. We obtain the asymptotic distributions almost exactly treating driving nonperturbatively. In the underdamped case, we exploit the underlying $SL_2$ symmetry to obtain the asymptotic state, and study the dynamics and fluctuations of energies and entropy. We further obtain the two-time correlation functions, and investigate the responses to drift and diffusion perturbations in the presence of driving.