Characterizations of intrinsically random dynamical systems

Abstract

We show that intrinsically random dynamical systems with the Prigogine operator Λ of the form of a random Laplace transform, can be characterized as Kolmogorov flows (K-flows). We also obtain a spectral characterization in the language of the Weyl commutation relation. As a consequence we conclude that the dynamical system is intrinsically random if and only if its Liouvillian and time operators form a Schrödinger couple.