Non-Markovian entropy production fluctuation theorem driven by a time-dependent electric field

TL;DR

This paper investigates the non-Markovian entropy production fluctuation theorem for charged particles under a time-dependent electric field, demonstrating the theorem's validity despite additional forces and analyzing specific cases with Gaussian trajectories.

Contribution

It extends the fluctuation theorem framework to non-Markovian systems influenced by time-dependent electric fields, showing the invariance of Kubo's FDT and deriving Gaussian probability densities.

Findings

Kubo's second FDT remains valid with an induced electric force.

The detailed fluctuation theorem holds for the total entropy production.

Explicit analysis of Ornstein-Uhlenbeck friction and oscillating electric fields.

Abstract

Fluctuation theorems are key to understanding both fundamental and applied aspects of non-equilibrium thermodynamics of small systems. We study the non-Markovian entropy production fluctuation theorem for the diffusion process of charged particles in a gas inside a harmonic potential and under the action of a time-dependent electric field, using a generalized Langevin equation. By considering the influence of the electric field on both the tagged Brownian particle and the bath particles, an "induced" electric force arises. Despite the additional force, we demonstrate that Kubo's second fluctuation-dissipation theorem (FDT) remains unchanged. The FDT allows us to obtain the Gaussian probability density for the position along a single stochastic trajectory, which is the key to demonstrating the validity of the detailed fluctuation theorem (DFT) for the total entropy production. We study the specific result of an Ornstein-Uhlenbeck-type friction memory kernel and an oscillating electric field, and analyze the average work and entropy production in different parameter regimes.