New progress in the principle of nonequilibrium statistical physics

Abstract

In recent years, a new fundamental equation of nonequilibrium statistical physics was proposed in place of the Liouville equation. That is the anomalous Langevin equation in Γ space or its equivalent Liouville diffusion equation of time-reversal asymmetry. This equation reflects that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality and the law of motion of statistical thermodynamics is stochastic in essence, but does not obey the Newton equation of motion, though it is also constrained by dynamics. The stochastic diffusion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this equation, the BBGKY diffusion equation hierarchy was presented, the hydrodynamic equations, such as the generalized Navier-Stokes equation, the mass drift-diffusion equation and the thermal conductivity equation have been derived succinctly. The unified description of all three level equations of microscopic, kinetic and hydrodynamic was completed. Furthermore, a nonlinear evolution equation of Gibbs and Boltzmann nonequilibrium entropy density was constructed, and the existence of entropy diffusion was predicted. The evolution equation shows that the change of nonequilibrium entropy density originates together from drift, diffusion and source production. Entropy production is manifestations of the law of entropy increase. Entropy diffusion governs the approach to equilibrium. All these derivations and results are unified and rigorous from the new fundamental equation without adding any extra assumption. In this review, an overview on the above main ideas, methods and results is given, and the international new progress in related problems of nonequilibrium statistical physics is summarized.