Irreversible quantum dynamics and the Hilbert space structure of quantum kinematics

General dynamics compatible with the Hilbert space structure of quantum kinematics are considered. The general form of dynamics which preserve the set of closed linear submanifolds (i.e., properties) is deduced. Since the orthogonality relation is not necessarily preserved, the result generalizes Wigner’s theorem and provides a model of some irreversible phenomena like spin relaxation, damped oscillator, etc. Connections with quantum logic and with statistical mechanics are presented.