Stochastic processes and dynamical systems in measure spaces are defined as classes of random variables in the Doob sense. Markov processes which are ergodic iato a “strong” sense are shoiwn to be suitable models for the thermodynamic irreverisilitiy. These processes are isomorphic, in the Doob sense, with Kolmogorov dynamical systems into the speces of trajectories. In this approach, we show that the Misra-Prigogine-Courbage theory of irreversibility can be formulated as a change of representation, from strong egodic. Markov processes to dynamical systems into the space of trajectories. The physical meaning is that all strong ergodic Markov processes, describing experimentally observed irreversibility, can be formally presented as unitary “superdynamics”.
Tiberiu Popoviciu Institute of Numerical Analysis
University of Pitești
N. Suciu, (2000), On the Misra-Prigogine-Courbage theory of irreversibility 2. The existence of the nonunitary similarity, Buletin ştiintific, Seria Mat.şi Inf. (Univ. Piteşti), 6, 213-222.
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 I. Antoniou and S. Tasaki, Generalized Spectral Decomposition of the β-adic Baker’s Transformation and Intrinsec Irreveribility, Physica A, 190, 303-329, 1992.
 I. Antoniou and K. E. Gustafson, From Probabilistic Description to Deterministic Dynamics, Physica A 179, 153-166, 1993.
 I. Antoniou and I. Prigogine, Intrinsec Irreversibility and Integrability of Dynamics, Physica A 192, 443-464, 1993.
 I Antoniou and S. Tasaki, Generalized Spectral Decomposition of Mixing Dynamical Systems, Int. J. Quantum Chem., 46, 425-474, 1993.
 I. Antoniou and K. E. Gustafson, I From Irreversibile Markov Semigroups to Chaotic Dynamics, Physica A 236, 296-308, 1997.
 I. Antoniou, K. E. Gustafson and Z. Suchanecki, On the Inverse Problem of Statistical Physics: From Irreversible Semigroups to Chaotic Dynamics, Physica A 256, 345-361, 1998.
 M. Courbage, On Boltzmann Entropy and Coarse-Graining for Classical Dynamical Systems, in Information Dynamics, ed. H. Atmanspacher and H. Scheingraber, Plenum New York, 1991.
 I. Cornfeld, S. Fomin and Ya. G. Sinai, Ergodic Theory, Springer, Berlin, 1982.
 C. Gardiner, Handbook of Stochastic Methods (for Physic, Chemstry and Natural Science), Springer, Berlin, 1983.
 N. A Friedman and D. S. Ornstein, On Isomorphism of Weak Bernoulli Transformations, Adv. Math. 5 (1971), 365-394.
 S. Goldstein, J. L. Lebowitz and E. Presutti, Stationary Markov Chains, in Fritz, J. J. L. Lebowitz and D. Szasz, editors, Rigorous results in statistical mechanics and quantum field theory, Colloquia Matematica Societatis Janos Bolyai, 27, North Holland, Amsterdam, 1981.
 M. Iosifescu and P. Tăutu, Stochastic Processes and Applicationsin Biology and Medicine. I. Theory, Editura Academiei, București and Springer, Berlin, 1973, 1970.
 A. Kolmogorov and S. Fomine, Elementes de la theorie des fonctions et de l’analyse fonctionelle, Mir. Moscou. 1975.
 A. Lasota and M. C. Meckey, Probabilistic Properties of Deterministic Systems, Springer, New York, 1985; Second edition and A. Lasota and M. C. Meckey, Chaos Fractals, and Noise, Stochastic Aspects of Dynamics, Springer, New York, 1994.
 M. C. Mackey, The Dynamic Origin of Increasing Entropy, Rev. Modern Pgys., 61, 4 (1989), 981-1016.
 P. Malliavin, Integration and Probability, Springer, New York, 1995.
 R. McCabe and P. Schields, A Class of Markov Shifts which are Bernoullu Shifts, Adv. Mat., 6 (1971), 323-328.
 B. Misra, I. Prigogine and M. Courbage, I From Deterministic Dynamics to Probabilistic Description, Physica 98A (1979), 1-26.
 G. Nicolis and C. Nicolis, Chaotic Dynamics, Markovian Coarse-Graining and Information, Physica A, 163 (1990), 215-231.
 D. S. Ornstein and P. C. Shields, Mixing Markov Shifts of Kernel Type are Bernoulli, Advances in Mathematics, 10 (1973), 143-146.
 V. A. Rokhlin, Exact Endomorphisms of Lebesque Spaces, Am. Math. Soc. Transl., (2) 39 (1964), 1-36.
 Ya. G. Sinai, Introduction to Ergodic Theory, Princeton, Univ. Press., 1976.
 N. Suciu and A. Georgescu, On the Misra-Prigogine-Courbage Theory of Irreversibility, Bul. Șt. Univ. Pitești, Seria Mat. Inf. 2 (1990), 169-188.
 B. Sz-Nagy and C. Foiaș, Harmonic Analyse of Operators in Hilbert Spaces, North-Holland, Amsterdam, 1970.
 N. G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1981.
 A. D. Wentzell, A Course in the Theory of Stochastic Processes, McGraw-Hill, New York, 1981.