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Exact equation for classical many‐body systems: Passage from dynamics to equilibrium
Author(s) -
Zakharov A. Yu.
Publication year - 2016
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.25008
Subject(s) - integro differential equation , boltzmann equation , classical mechanics , physics , differential equation , burgers' equation , partial differential equation , integral equation , fokker–planck equation , fisher's equation , statistical physics , first order partial differential equation , mathematical analysis , mathematics , quantum mechanics
The exact basic equation of motion for the microscopic density of system of interacting particles is derived. In this derivation, no probabilistic hypotheses or assumptions are used. This integro‐differential equation is the equation of motion of nonlinear classical scalar field with respect to the microscopic density. The possible mechanisms of transition of many‐particle system in equilibrium state are discussed. On the basic equation, the exact integral equation for the equilibrium spatial distribution of the particles is obtained. It is shown that the Boltzmann distribution and the Vlasov equation are special cases of this integral equation. The wave equation for almost homogeneous systems with interparticle interactions is obtained. Effect of interparticle interactions on the dispersion law of sound is established. © 2015 Wiley Periodicals, Inc.