Dynamics of stochastic systems and peculiarities of measurements in them

Abstract

One calls attention to the fact that the stochastic physical systems are not random completely. They have both random and regular components of their evolution. Dynamic system is considered to be a special case of physical system with vanishing stochastic component of evolution. Mathematical technique for description of regular evolution component of physical systems (stochastic and deterministic) is constructed. The regular component of the system S evolution is described explicitly by the statistical average system <S>, which is a continuous dynamic system. The action for <S> is reduced to the form of the action for a set of interacting identical deterministic systems S_d. The form of interaction of S_d describes implicitly the character of the stochastic component of S evolution. Interplay between the physical system S and the statistical average system <S> in the measurement process is discussed. There are at least two different kind of measurement: single measurements (S-measurements) connected with measurements in S and mass measurements (M-measurements) connected with measurements in <S>. Conventional identification of S-measurement and M-measurement is a source of many misunderstandings and paradoxes.