2004/04/22 by Pierre-Henri Chavanis
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Fokker–Planck equation #Lattice (music) #Limit (mathematics) #Mathematical analysis #Mathematics #Partial differential equation #Physics #Planck #Quantum #Quantum mechanics #Statistical Mechanics and Entropy #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physa.2004.03.077
published as Physica A, 340, 57 (2004)
openalex publication_date 2004/04/22 · arxiv created 2005/04/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a new class of Fokker-Planck equations associated with an effective generalized thermodynamical framework. These equations describe a gas of Langevin particles in interaction. The free energy can take various forms which can account for anomalous diffusion, quantum statistics, lattice models... When the potential of interaction is long-ranged, these equations display a rich structure associated with canonical phase transitions and blow-up phenomena. In the limit of short-range interactions, they reduce to Cahn-Hilliard equations.