par Misra, Baidyawath ;Prigogine, Ilya ;Courbage, Maurice
Référence Physica A. Statistical and Theoretical Physics, 98, 1-2, page (1-26)
Publication Publié, 1979
Article révisé par les pairs
Résumé : 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?It is generally accepted that probabilistic processes can arise from deterministic dynamics only through a process of “coarse graining” or “contraction of description” which inevitably involves a loss of information. In this work we present an alternative point of view toward the relation between deterministic dynamics and probabilistic descriptions. Speaking in general terms, we demonstrate the possibility of obtaining (stochastic) Markov processes from deterministic dynamics simply through a “change of representation” which involves no loss of information provided the dynamical system under consideration has a suitably high degree of instability of motion. The fundamental implications of this finding for statistical mechanics and other areas of physics are discussed. From a mathematical point of view, the theory we present is a theory of invertible, positivity preserving and necessarily nonunitary similarity transformations that convert the unitary groups associated with deterministic dynamics to contraction semigroups associated with stochastic Markov processes. We explicitly construct such similarity transformations for the so-called Bernoulli systems. This construction illustrates also the construction of the so-called Lyapounov variables and the operator of “internal time” which play an important role in our approach to the problem of irreversibility. The theory we present can also be viewed as a theory of entropy increasing evolutions and their relation to deterministic dynamics. The possibility of obtaining entropy increasing evolutions from deterministic dynamics through a nonunitary similarity transformation is concretely illustrated in the present work.