Intrinsic Stochasticity and Irreversibility of Classical Quantum Systems

Abstract

This contribution is devoted to the question of the relation between the deterministic laws of dynamics and probabilistic descriptions of physical processes. This problem has been the object of many attempts. It is generally accepted that probabilistic processes can arise from deterministic dynamics through a process of “coarse-graining”, “contraction of the description” or by introducing extra dynamic approximations like the “molecular chaos”. In this short communication I will summarize recent results obtained by B. Misra, I. Prigogine and myself [1], [2], [3] on an alternative approach to this problem which consists in obtaining stochastic processes from deterministic dynamics by a similarity invertible linear transformations acting on the space of the distribution functions, when the dynamics is inherently random or unstable. In this case the irreversibility is obtained by a change of representation without any supplementary hypothesis.