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On the Statistical Theory of Nonequilibrium Processes
Author(s) -
Magalinskij V. B.,
Terletskij Ja. P.
Publication year - 1960
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19604600507
Subject(s) - langevin equation , physics , statistical physics , brownian motion , master equation , equations of motion , fokker–planck equation , classical mechanics , diffusion process , nonlinear system , anomalous diffusion , statistical mechanics , mathematics , differential equation , quantum mechanics , knowledge management , innovation diffusion , computer science , quantum
A general method is worked out on the basis of principles of Gibbs' statistical mechanics which allows to find stationary probabilities and transition probabilities for physical quantities provided either the behaviour of their mean values or the general form of corresponding equations of motion (Langevin equations) is known. The proposed method is free from ordinary restrictions of the theory of fluctuations and Brownian motion, such as, modest fluctuations, linearity of phenomenological equations, Markov's character of the random process and is applicable also to postacting systems. The method is applied to some physical systems. For the system, described by a non‐linear equation of motion the general coordinate‐velocity equation of motion of the transition probability density is obtained. This equation coincides with the well‐known Einstein‐Fokker‐Plank coordinate‐velocity equation in the case of linear friction law. The diffusion equation is obtained for the electrical circuit consisting of capacity and nonlinear resistance. Its general solution is found.