Abstract
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.
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