Stochastic Echo Phenomena in Nonequilibrium Systems

TL;DR

This paper explores the stochastic echo phenomenon in nonequilibrium thermodynamic systems, deriving optimal protocols for time reversal, and demonstrating perfect echo in harmonic oscillators and systems with nonconservative forces.

Contribution

It introduces a method to control nonequilibrium systems to exhibit time-reversed behavior using optimal protocols, revealing new insights into time irreversibility.

Findings

Perfect stochastic echo observed in harmonic oscillators under time-dependent driving.

Any system with a time-independent nonconservative force has a dual system with perfect echo.

The study offers a new perspective on the irreversibility of nonequilibrium processes.

Abstract

A thermodynamic system is driven into a nonequilibrium condition when a time-dependent force or a nonconservative force represented by a protocol $\lambda(t)$ is applied. Such a system is time irreversible in the sense that the motion under a protocol $\lambda(0\leq t\leq \tau)$ and the time-reversed motion under $\lambda(\tau-t)$ are not equally probable. We investigate a stochastic echo phenomenon in which a system is controlled by an optimal protocol to display the time-reversed motion. The optimal protocol is derived for a Langevin system. For the time-dependent driving case, simple harmonic oscillator systems are found to display the perfect stochastic echo phenomenon. We also show that any system driven by a time-independent nonconservative force has a dual system displaying the perfect stochastic echo phenomenon. Our study provides a novel perspective on the time-irreversibility of nonequilibrium systems.