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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 G space or its equivalent Liouville diffusion equa-tion 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 irreversi-bility. Starting from this equation,the BBGKY diffusion equation hierarchy was presented,the hydrodynamic equa-tions,such as the generalized Navier-Stokes equation,the mass drift-diffusion equation and the thermal conductivity equation have been derived succinctly. The unified descrip-tion 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 entro-py diffusion was predicted. The evolution equation shows that the change of nonequilibrium entropy density originates together from drift,diffusion and source production. Entro-py production is manifestations of the law of entropy in-crease. Entropy diffusion governs the approach to equilib-rium. All these derivations and results are unified and rigor-ous 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 interna-tional new progress in related problems of nonequilibrium statistical physics is summarized.