Study On Entropy Production Of Nonequilibrium System By Fokker-Planck Equation

As the notion of entropy plays an important role in the progress of thermodynamics statisticmechanics, the entropy production of a nonequilibrium system is recognized as a hot issueof the international frontier areas. Entropy production rate of nonequilibrium systemsdescribed by Fokker-Planck equation is studied. The approach is based on the expressionof the entropy production rate advanced by Schnakenberg from a master equation and thusneeds the information of the transition rate of the concerned system. We obtain thetransition rate by using a conditional probability that can be derived from a Fokker-Planckequation easily. Thus a new formula which can be used to calculate the entropy productionrate of a nonequilibrium system, with continuous states, descriped by a Fokker-Planckequation is obtained. Our expression is widely applicable, and it is more operable orcomputable than that advanced by Schnakenberg.After the formula is obtained, we try to calculate some peculiar cases of Fokker-Plancksystems as application examples of the new method proposed in this paper, the first one isthe Fokker-Planck equation with constant diffusion function, including the Smoluchowskiequation and the Ornstein-Uhlenbeck process. We also have a discussion on the specialcase which can lead to stationary state with power-law distribution. The result of abovecases is as the same as that some researchers developed before by some measures differentfrom that showed here. This fact shows the correctness and the effectiveness of our methodin some extents.