Stochastic processes and dynamical systems in measure spaces are defined as classes of random variables in the Doob sense. Markov processes which are ergodic into a “strong” sense are shown to be suitable models for the thermodynamic irreveribility. These processes are also isomorphic, in the Doob sense, with Bernoulli dynamical systems defined into the space of trajectories. In this approach, we show that the Misra Prigogine-Courbage theory of irreversibility can be formulated as a change of representation of strong ergodic Markov processes. The physically meaning is that all experimentally observed strong ergodic Markov processes can be “lifted” to a unitary “superdynamics”.
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
Faculty of Sciences, University of Pitești
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