Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production

摘要

The solution to nonlinear Fokker-Planck equation is constructed in terms ofthe minimal Markov semigroup generated by the equation. The semigroup isobtained by a purely functional analytical method via Hille-Yosida theorem. Theexistence of the positive invariant measure with density is established and aweak form of Foguel alternative proven. We show the equivalence amongself-adjoint of the elliptic operator, time-reversibility, and zero entropyproduction rate of the stationary diffusion process. A thermodynamic theory fordiffusion processes emerges.