by R. F. Streater in "Stochastic Partial Differential Equations", Ed. A. Etheridge, Cambridge Univ. Press, 1995.
We consider how to add noise to a non-linear system in a way that obeys the laws of thermodynamics. We treat a class of dynamical systems which can be expressed as a (possibly non-linear) motion through the set of probability measures on a sample space. Thermal noise is added by coupling this random system to a heat-particle distributed according to a Gibbs state. The theory is illustrated by the Brussellator, where it is shown that the noise converts a limit cycle into a global attractor. In the linear case it is shown that every Markov chain with transition matrix close to the identity is obtained by coupling to thermal noise with a bistochastic transition matrix.
See my book, STATISTICAL DYNAMICS, and links to my other works on the subject, and later work on information geometry.
Go to my HOME PAGE for more links.
© by Ray Streater, 13/6/2000.