一般最小扩散过程的统计热力学：常数、不变密度、可逆性和熵产生
Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production
摘要：
利用非线性Fokker-Planck方程生成的极小Markov半群构造了该方程的解。利用Hille-Yosida定理，用纯泛函分析方法得到了该半群.建立了具有密度的正不变测度的存在性，证明了Foguel替代的一个弱形式。我们证明了自伴的椭圆算子，时间可逆性，零熵产生率的平稳扩散过程之间的等价性。扩散过程的热力学理论出现。
英文摘要：
The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence of the positive invariant measure with density is established and a weak form of Foguel alternative proven. We show the equivalence among self-adjoint of the elliptic operator, time-reversibility, and zero entropy production rate of the stationary diffusion process. A thermodynamic theory for diffusion processes emerges.
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