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

摘要

Fluctuation theorem is one of the major achievements in the field ofnonequilibrium statistical mechanics during the past two decades. Steady-statefluctuation theorem of sample entropy production rate in terms of largedeviation principle for diffusion processes have not been rigorously proved yetdue to technical difficulties. Here we give a proof for the steady-statefluctuation theorem of a diffusion process in magnetic fields, with explicitexpressions of the free energy function and rate function. The proof is basedon the Karhunen-Lo\'{e}ve expansion of complex-valued Ornstein-Uhlenbeckprocess.