Statistical dynamics with thermal noise

by R. F. Streater in "Stochastic Partial Differential Equations", Ed. A. Etheridge, Cambridge Univ. Press, 1995.

ABSTRACT

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.

REMARKS

See my book, STATISTICAL DYNAMICS, and links to my other works on the subject, and later work on information geometry.