Breakdown of time reversal symmetry: intrinsic randomness, time operator, scattering. (English) Zbl 1147.82337

Summary: 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.


82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
47A40 Scattering theory of linear operators