2018/01/24 by P. Maynar, M. I. García de Soria, J. Javier Brey · 16 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Burgers' equation #Classical mechanics #Distribution (mathematics) #Gas Dynamics and Kinetic Theory #Generalization #Geometry #Hard spheres #Kinetic energy #Kinetic theory #Mathematical analysis #Mathematical physics #Mathematics #Monotonic function #Partial differential equation #Particle Dynamics in Fluid Flows #Physics #Quantum mechanics #SPHERES #Statistical mechanics #Statistical physics #Tensor (intrinsic definition) #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-018-1971-7
published in Journal of Statistical Physics 170(5), 999-1018 (Springer Science+Business Media)
arxiv created 2018/01/24 · openalex publication_date 2018/01/30 · arxiv updated 2018/03/14 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/09
A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account and it is supposed to be valid up to moderate densities. From the equation, balance equations for the hydrodynamic fields are derived, identifying the collisional transfer contributions to the pressure tensor and heat flux. A Lyapunov functional, H[f], is identified. For any solution of the kinetic equation, H decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a the density field consistent with equilibrium statistical mechanics.