Dynamics of stochastic systems and peculiarities of measurements in them

Yuri A.Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences,
101, bild.1 Vernadskii Ave., Moscow, 119526, Russia.
e-mail: rylov@ipmnet.ru}

Updated March 28, 2002


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. Determinitic physical 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 costructed. The regular component of the system S evolution is described explicitly by the statistical average system <S>, which is a deterministic physical (dynamic) system. The action A_<S> for <S> is reduced to the form of the action A_S[S_d] for a set S[S_d]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 dynamic system S and the statistical average dynamic 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>. Confusion of S-measurement and M-measurement leads to misunderstandings and paradoxes.


(There is the  text of the paper in English and in Russian in the form of a postscript file)