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 (?) space or its equivalent Liouville diffu...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 (?) space or its equivalent Liouville diffusion equation of time-reversal asymmetry. This equation reflects that the form of motion of particles in statistical thermody-namic 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 irre-versibility. 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展开更多
Some derivations based on the anomalous Langevin equation in Liouville space (i.e. Γ space) or its equivalent Liouville diffusion equation of time reversal asymmetry are presented. The time rate of change, the balanc...Some derivations based on the anomalous Langevin equation in Liouville space (i.e. Γ space) or its equivalent Liouville diffusion equation of time reversal asymmetry are presented. The time rate of change, the balance equation, the entropy flow, the entropy production and the law of entropy increase of Gibbs nonequilibrium entropy and Boltzmann nonequilibrium entropy are rigorously derived and presented here. Furthermore, 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 entropy density originates from not only drift, but also typical diffusion and inherent source production. Contrary to conventional knowledge, the entropy production density σ ≥0 everywhere for all the inhomogeneous systems far from equilibrium cannot be proved. Conversely, σ may be negative in some local space of such systems.展开更多
Considering that thermodynamic irreversibility, the principle of entropy increase and hydrodynamic equations cannot be derived rigorously and in a unified way from the Liouville equations, the anomalous Langevin equat...Considering that thermodynamic irreversibility, the principle of entropy increase and hydrodynamic equations cannot be derived rigorously and in a unified way from the Liouville equations, the anomalous Langevin equation in Liouville space or its equivalent generalized Liouville equation is proposed as a basic equation of statistical physics. This equation reflects the fact that the law of motion of statistical thermodynamics is stochastic, but not deterministic. From that the nonequilibrium entropy, the principle of entropy increase, the theorem of minimum entropy production and the BBGKY diffusion equation hierarchy have been derived. The hydrodynamic equations, such as the generalized Navier-Stokes equation and the mass drift-diffusion equation, etc. have been derived from the BBGKY diffusion equation hierarchy. This equation has the same equilibrium solution as that of the Liouville equation. All these are unified and rigorous without adding any extra assumption. But it is difficult to prove that展开更多
文摘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 (?) space or its equivalent Liouville diffusion equation of time-reversal asymmetry. This equation reflects that the form of motion of particles in statistical thermody-namic 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 irre-versibility. 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
文摘Some derivations based on the anomalous Langevin equation in Liouville space (i.e. Γ space) or its equivalent Liouville diffusion equation of time reversal asymmetry are presented. The time rate of change, the balance equation, the entropy flow, the entropy production and the law of entropy increase of Gibbs nonequilibrium entropy and Boltzmann nonequilibrium entropy are rigorously derived and presented here. Furthermore, 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 entropy density originates from not only drift, but also typical diffusion and inherent source production. Contrary to conventional knowledge, the entropy production density σ ≥0 everywhere for all the inhomogeneous systems far from equilibrium cannot be proved. Conversely, σ may be negative in some local space of such systems.
文摘Considering that thermodynamic irreversibility, the principle of entropy increase and hydrodynamic equations cannot be derived rigorously and in a unified way from the Liouville equations, the anomalous Langevin equation in Liouville space or its equivalent generalized Liouville equation is proposed as a basic equation of statistical physics. This equation reflects the fact that the law of motion of statistical thermodynamics is stochastic, but not deterministic. From that the nonequilibrium entropy, the principle of entropy increase, the theorem of minimum entropy production and the BBGKY diffusion equation hierarchy have been derived. The hydrodynamic equations, such as the generalized Navier-Stokes equation and the mass drift-diffusion equation, etc. have been derived from the BBGKY diffusion equation hierarchy. This equation has the same equilibrium solution as that of the Liouville equation. All these are unified and rigorous without adding any extra assumption. But it is difficult to prove that
