ON THE INVERSE PROBLEM OF STATISTICAL PHYSICS - FROM IRREVERSIBLE SEMIGROUPS TO CHAOTIC DYNAMICS

We show that all measure preserving stationary Markov processes arise as projections of Kolmogorov dynamical systems which have positive ent ropy production and an prototypes of chaos. This result not only contr ibutes to the clarification of the relation of dynamics with stochasti c processes but also shows the physical significance of the Misra-Prig ogine-Courbage theory of irreversibility in the more general context o f the inverse problem of statistical physics. Because we want positivi ty preserving transformations, our procedure although analogous to the Sz-Nagy-Foias Dilation theory has a different viewpoint, that of posi tive dilations. (C) 1998 Elsevier Science B.V. All rights reserved.