The Large Deviation Principle and Steady-state Fluctuation Theorem for the Entropy Production Rate of a Stochastic Process in Magnetic Fields

TL;DR

This paper rigorously proves the steady-state fluctuation theorem for the entropy production rate in diffusion processes under magnetic fields, providing explicit formulas for key functions using advanced stochastic analysis techniques.

Contribution

It offers the first rigorous proof of the fluctuation theorem for such processes, with explicit expressions derived via Karhunen-Loève expansion.

Findings

Proof of the steady-state fluctuation theorem for diffusion in magnetic fields

Explicit formulas for free energy and rate functions

Application of Karhunen-Loève expansion to complex Ornstein-Uhlenbeck processes

Abstract

Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. Steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes have not been rigorously proved yet due to technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Lo\'{e}ve expansion of complex-valued Ornstein-Uhlenbeck process.