On the Statistical Theory of Nonequilibrium Processes

✍ Scribed by V. B. Magalinskij; Ja. P. Terletskij

• Publisher: John Wiley and Sons
• Year: 1960
• Tongue: English
• Weight: 558 KB
• Volume: 460
• Category: Article
• ISSN: 0003-3804
• DOI: 10.1002/andp.19604600507

✦ Synopsis

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, Mark ov'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 thegeneral coordinate-velocity equation of motion of the transition probability density is obtained. This equation coincides with the well-known E i n s t e i n -F o k k e r -P l a n k 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. l) J. W. Gibbs, Principles of Statistical Mechanics (Collected Works, l), New York, 2, V. V. V l a d i m i r s k i j , J. Exptl. Theoret. Phys. (USSR) 12, 199 (1942). 3, V. V. V l a d i m i r s k i j and J a . P. T e r l e t s k i j , J. Exptl. Theoret. Phys. (USSR) *) Ja. P. T e r l e t s k i j , ,&maMusecKne II cTaTucTn9ecme ~~K O H ~I ~H ~H K H (Dyna-5 , Ja. P. T e r l e t s k i j , Nuovo Cimento 7, 308 (1958).