2019/11/15 by Nikolaos Kalogeropoulos, Kalogeropoulos, Nikolaos
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1911.06626
openalex publication_date 2019/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an argument which intends to explore a potential geometric origin of a class of non-linear Fokker-Planck equations related to the mesoscopic behavior of systems conjecturally described by the q-entropy. We argue that the appearance of the non-linear term(s) in such equations can be ascribed to the fact that the effective mesoscopic metric describing the behavior of the underlying system may not be the originally chosen one, but a conformal deformation of it. Motivated by Liouville's theorem, we highlight the role played by the scalar curvature of conformally related metrics in establishing such a non-linear Fokker-Planck equation.