Derivation of the phenomenological equations from the master equation: I. Even variables only

✍ Scribed by N.G. Van Kampen

• Publisher: Elsevier Science
• Year: 1957
• Weight: 672 KB
• Volume: 23
• Category: Article
• ISSN: 0031-8914
• DOI: 10.1016/s0031-8914(57)94131-9

✦ Synopsis

Instituut voor theoretische fysica, Rijksuniversiteit te Utrecht, Nederland

Synopsis

The 'master equation' describes the behaviour of a macroscopic system in terms of a time dependent probability distribution. It is here shown that, if the initial distribution is concentrated in a small region, it moves toward equilibrium without spreading. Thus the stochastic process described by the master equation is observed as a deterministic process by an observer whose observations are too coarse to observe the fluctuations. This is the process t;o which the usual phenomenological equations refer. With the aid of appropriate approximations one finds in this way the well-known linear regression equations, including Onsager's reciprocal relations. *) Originally it was called 'microscopic reversibility' 8), but this name is somewhat confusing, because (4) does not involve microscopic quantities, nor is it identical with -although a consequence of -the time reversibility of the microscopic equations of motion.