刘维空间反常朗之万方程为基础的非平衡统计物理

考虑到热力学不可逆性和流体力学方程不能严格统一地从刘维方程推导出，本文提出了刘维空间的反常朗之万方程作为统计物理的基本方程．这个方程反映了粒子在动力学中遵守的可逆的确定性的运动规律到统计热力学系统中变为不可逆的随机性的．由这个基本方程可严格推导出非平衡热力学基本方程、嫡增长原理、最小墒产生定理以及流体力学方程如广义纳维尔－斯托克斯方程、质量漂移－扩散方程等．所有这些都是统一的自洽的．但是难以证明所有非均匀远离平衡的孤立系统中的熵产生密度在各处都满足σ≥０

Nonequilibrium Statistical Physics Subject to the Anomalous Langevin Equation in Liouville Space

Considering that thermodynarmic irreversibility and hydrodynamic equations can not be derived rigorously and unifiedly from the Liouville equations, the anomalous Langevin equation in the Liouville space is proposed as a fundamental equation of statistical physics. This equation reflects that the law of motion of particles obeying reversible, deterministic laws in dynamics becomes irreversible and stochastic in thermodynamics. From this the fundamental equations of nonequilibrium thermodynamics, the principle of entropy increase and the theorem of minimum entropy production have been derived. The hydrodynamic equations, such as the generalized Navier-Stokes equation and the mass drift-diffusion equation etc. have been derived rigorously from the kinetic kinetic equation which is reduced from the anomalous Langevin equation in Liouville space. All these are unified and self consistent. But it is difficult to prove that entropy production density σ can never be negative everywhere for all the isolated inhomogeneous systems far from equilibrium.