Stochastic entropy production in diffusive systems

Abstract

Computing the stochastic entropy production associated with the evolution of a stochastic dynamical system is a well-established problem. In a small number of cases such as the Ornstein-Uhlenbeck process, of which we give a complete exposition, the distribution of entropy production can be obtained analytically. For a general potential it is much harder. A recent development in solving the Fokker-Planck equation, in which the solution is written as a product of positive functions, addresses any system governed by the condition of detailed balance, thereby permitting nonlinear potentials. Using examples in one and higher dimension, we demonstrate how such a framework is very convenient for the computation of stochastic entropy production in diffusion processes.