The present work is devoted to the following question: What is the relation between the deterministic laws of dynamics and probabilistic description of physical processes?

In a previous paper, Misra, Prigogine and Courbage have shown that each Bernoulli dynamical system may be associated through positivity preserving similarity transformations to a stochastics Markov process. Here we give generalized baker transformarmations are necessarily distinct. processes...

Koopman's Lemma states that if a flow Tt is measure preserving for a measure μ on a constant energy surface Ω, then the flow generates a one parameter family of unitary operators Ut on L2 (Ω, μ). We show here a converse, namely that under certain (physically motivated) conditions a unitary...

We extend to Bernoulli systems the explicit construction (elaborated previously for the baker transformation) of non-unitary, invertible transformations Λ, which associate Markovian processes admitting an H-theorem with the unitary dynamical group, through a similarity relation. We characterize...

It is argued that a restriction of the set of observables is necessary in order to effect “reduction of the wave packet”. This restriction leads to an irreversible evolution for the system plus apparatus (S + A), a possibility which exists only when the apparatus is an infinite quantum...