An explicit approach to the Λ-operator and the H-theorem in the Prigogine theory of irreversibility

Abstract

Abstract A reformulation of the Prigogine theory of irreversible dynamical systems is given. In contrast to the previous works a stochastic integral with respect operator valued martingales is employed here. This approach provides a mathematically rigorous and simple construction of the Λ operator for dynamical flows. It has an explicit random character. We derive also the Boltzmann H-theorem explicitly from the properties of the semigroup only. Finally, the form of the Boltzmann kinetic equation for the irreversible dynamics is found.