2016/10/31 by Massimo Tessarotto, Tessarotto, Massimo, M. Mond +4
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Phase Equilibria and Thermodynamics #Statistical Mechanics and Entropy #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1610.09872
arxiv created 2016/10/31 · openalex publication_date 2016/10/31 · arxiv updated 2016/11/01 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28
Based on the recently-established Master kinetic equation and related Master constant H-theorem which describe the statistical behavior of the Boltzmann-Sinai classical dynamical system for smooth and hard spherical particles, the problem is posed of determining a microscopic statistical description holding for an incompressible Navier-Stokes fluid. The goal is reached by introducing a suitable mean-field interaction in the Master kinetic equation. The resulting Modified Master Kinetic Equation (MMKE) is proved to warrant at the same time the condition of mass-density incompressibility and the validity of the Navier-Stokes fluid equation. In addition, it is shown that the conservation of the Boltzmann-Shannon entropy can similarly be warranted. Applications to the plane Couette and Poiseuille flows are considered showing that they can be regarded as final decaying states for suitable non-stationary flows. As a result, it is shown that an arbitrary initial stochastic 1-body PDF evolving in time by means of MMKE necessarily exhibits the phenomenon of Decay to Kinetic Equilibrium (DKE), whereby the 1-body PDF asymptotically relaxes to a stationary and spatially-uniform Maxwellian PDF.