Uniform formalism for description of dynamic and stochastic systems

Yuri A. Rylov

Published Mar 28, 2006• 2 citations

Abstract

The formalism of dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is primordially deterministic, seems to be unsuitable. The statistical ensemble of stochastic (or deterministic) systems is considered to be the main object of dynamics. At such an approach one can describe deterministic, stochastic and quantum particles by means of the uniform technique. The quantum particle is described as a stochastic particle, i.e. without a reference to the quantum principles. Besides, by means of this technique one can describe classical inviscid fluid. There are four different versions of the formalism. One of versions uses equations, which describes evolution of the labelling (Lagrangian coordinates at fixed initial conditions for the density and the momentum density. These fixed initial conditions enter in the evolution equations. A nonuniqueness of irrotational flow and the mismatch between the velocity and the momentum density appear at this description. The mismatch is determined by the fluid vorticity and by some arbitrary parameter. Appearance of mismatch may be associated with the turbulence. The united formalism is purely dynamic. Even describing stochastic systems, it does not refer to probability and probabilistic structures.

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