Breakdown of Time-Reversal Symmetry: Intrinsic Randomness, Time Operator, Scattering

Abstract

Misra-Prigogine-Courbage theory of irreversibility is revisited on the basis of Nagy-Foiaş dilation theory and Halmos-Helson theory of invariant subspaces. Universal models for intrinsically random dynamics are given as well as equivalent conditions to the existence of internal time operators, where innovation processes and Lax-Phillips scattering appear in a natural way.