ON THE FUNDAMENTAL EQUATION OF NONEQUILIBRIUM STATISTICAL PHYSICS

In this paper we proposed a new fundamental equation of statistical ph ysics in place of the Liouville equation. That is the anomalous Langev in equation in Gamma space or its equivalent Liouville diffusion equat ion of time-reversal asymmetry, This equation reflects that the form o f motion of particles in statistical thermodynamic systems has the dri ft-diffusion duality and the law of motion of statistical thermodynami cs is stochastic in essence, but not completely deterministic. Startin g from this equation the BBGKY diffusion equation hierarchy, the law o f entropy increase, the theorem of minimum entropy production, the bal ance equations of Gibbs and Boltzmann nonequilibrium entropy are deriv ed and presented here. Furthermore we have derived a nonlinear evoluti on equation of Gibbs and Boltzmann nonequilibrium entropy density. To our knowledge, this is the first treatise on them. The evolution equat ion shows that the change of nonequilibrium entropy density originates together from drift, typical diffusion and complicated inherent sourc e production. Contrary to conventional viewpoint, the entropy producti on density sigma greater than or equal to 0 everywhere for any systems cannot be proved universally. Conversely, sigma may be negative in so me local space of some inhomogeneous systems far from equilibrium. The hydrodynamic equations, such as the generalized Navier-Stokes equatio n, the mass drift-diffusion equation and the thermal conductivity equa tion have been derived succinctly from the BBGKY diffusion equation hi erarchy. The Liouville diffusion equation has the same equilibrium sol ution as that of the Liouville equation. All these derivations and res ults are unified and rigorous from the new fundamental equation withou t adding any extra assumption.