2013/07/31 by Daniel Alpay, Alexander Sakhnovich, Lev Sakhnovich +1 · 5 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Algebra over a field #Fokker–Planck equation #Generalization #Geometry #Inner product space #Inverse #Mathematical analysis #Mathematical physics #Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Operator (biology) #Partial differential equation #Physics #Planck #Probability density function #Product (mathematics) #Pure mathematics #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Spectral Theory in Mathematical Physics #Statistical Mechanics and Entropy #Statistical physics #Statistics #Type (biology) #Vector space #math-ph #math.AP #math.MP #msc:35Q20 #msc:51K99 #msc:82B40
paper · pdf · doi:10.1007/978-3-319-10335-8
published in Operator theory (Springer Nature) · Minor text corrections are made in the second version. The paper is published in "Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes" Oper. Theory Adv. Appl. 244, 379--394, Birkhauser, 2015
openalex publication_date 2015/01/01 · arxiv created 2015/05/13 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15
We start with a global Maxwellian Mk, which is a stationary solution, with the constant total density (ρ(t)≡ \wt ρ), of the Fokker-Planck equation. The notion of distance between the function Mk and an arbitrary solution f (with the same total density \wt ρ at the fixed moment t) of the Fokker-Planck equation is introduced. In this way, we essentially generalize the important Kullback-Leibler distance, which was studied before. Using this generalization, we show local stability of the global Maxwellians in the spatially inhomogeneous case. We compare also the energy and entropy in the classical and quantum cases.