Thermodynamics of the General Diffusion Process: Time-Reversibility and Entropy Production

2002/01/01 by Hong Qian, Min Qian, Xiang Tang · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Mathematical Biology Tumor Growth #Statistical Mechanics and Entropy #math-ph #math.MP

paper · pdf · doi:10.1023/a:1015109708454

published as Journal of Statistical Physics, Vol. 107, pp. 1129-1141 (2002) · 23 pages

arxiv created 2002/01/01 · openalex publication_date 2002/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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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