The large deviation principle and steady-state fluctuation theorem for the entropy production rate of a stochastic process in magnetic fields

Abstract

Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. Steadystate 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-Loéve expansion of complex-valued 1 LDP of entropy production rate in magnetic fields 2 Ornstein-Uhlenbeck process.

Moderate and $L^p$ maximal inequalities for diffusion processes and conformal martingales

“…Interestingly, the results in this paper can also be used to establish the maximal inequalities for some high-dimensional processes. Here we consider the moderate maximal inequalities for the complex OU process, which is also an important kinetic model in statistical mechanics [26]. We recall the following definition [27,28].…”

Asymptotics of Sample Entropy Production Rate for Stochastic Differential Equations

“…The entropy production rate (EPR in short) is a key element of the second law of thermodynamics for open systems, see for instance [8,10,6,13,14]. In this paper we characterize the asymptotic behaviors of the sample EPR for diffusion processes.…”