On the Fundamental Equation of Nonequilibrium Statistical Physics -- Nonequilibrium Entropy Evolution Equation and the Formula for Entropy Production Rate

摘要

In this paper we presented an overview on our works. More than ten years ago,we proposed a new fundamental equation of nonequilibrium statistical physics inplace of the present Liouville equation. That is the stochastic velocity type'sLangevin equation in 6N dimensional phase space or its equivalent Liouvillediffusion equation. This equation is time-reversed asymmetrical. It shows thatthe form of motion of particles in statistical thermodynamic systems has thedrift-diffusion duality, and the law of motion of statistical thermodynamics isexpressed by a superposition of both the law of dynamics and stochasticvelocity and possesses both determinism and probability. Hence it is differentwith the law of motion of particles in dynamical systems. Starting from thisfundamental equation the BBGKY diffusion equation hierarchy, the Boltzmanncollision diffusion equation, the hydrodynamic equations such as the massdrift-diffusion equation, the Navier-Stokes equation and the thermalconductivity equation have been derived and presented here. What is moreimportant, we first constructed a nonlinear evolution equation ofnonequilibrium entropy density in 6N, 6 and 3 dimensional phase space,predicted the existence of entropy diffusion. This evolution equation revealsthat the time rate of change of nonequilibrium entropy density originatestogether from its drift, diffusion and production in space. Furthermore, wepresented a formula for entropy production rate (i.e. the law of entropyincrease), proved that internal attractive force in nonequilibrium system canresult in entropy decrease while internal repulsive force leads to anotherentropy increase, obtained an unified theoretical expression for thermodynamicdegradation and self-organizing evolution, and revealed that the entropydiffusion mechanism caused the system to approach to equilibrium.