Irreversible evolution in quantum logics (Q1200436)

The author presents a possible characterization of irreversible dynamics in the context of quantum logic. An analogous investigation of reversible dynamics was performed in a paper by \textit{V. Gorini} and the author [J. Math. Phys. 16, 667-669 (1975)]. The dynamical semigroup used here consists of certain linear endomorphisms of the linear span of the state space. As existence and uniqueness of the observables are postulated, the observables form a normed linear space. The author introduces the Heisenberg and the Schrödinger pictures in this logic scheme and proves their equivalence. Regrettably, the paper lacks any reference to recent research, and also a comparison to the corresponding section of the monograph of \textit{E. G. Beltrametti} and \textit{G. Cassinelli} [The logic of quantum mechanics (1981; Zbl 0504.03026)] would have been useful.