ON FUNDAMENTAL EQUATION OF STATISTICAL PHYSICS (II) - NONEQUILIBRIUM ENTROPY AND ITS EVOLUTION EQUATION

Some derivations based on the anomalous Langevin equation in Liouville space (i. e. I' space) or its equivalent Liouville diffusion equation of time-reversal asymmetry are presented. The time rate of change, th e balance equation, the entropy flow, the entropy production and the l aw of entropy increase of Gibbs nonequilibrium entropy and Boltzmann n onequilibrium entropy are rigorously derived and presented here. Furth ermore, a nonlinear evolution equation of Gibbs nonequilibrium entropy density and Boltzmann nonequilibrium entropy density is first derived . The evolution equation shows that the change of nonequilibrium entro py density originates from not only drift, but also typical diffusion and inherent source production. Contrary to conventional knowledge, th e entropy production density sigma greater than or equal to 0 everywhe re for all the inhomogeneous systems far from equilibrium cannot be pr oved. Conversely, sigma may be negative in some local space of such sy stems.