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Randomness and Probability in Dynamical Theories: On the Proposals of the Prigogine School

Published online by Cambridge University Press:  01 April 2022

Robert W. Batterman
Robert W. Batterman*
Affiliation:
Department of Philosophy, Ohio State University
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Abstract

I discuss recent work in ergodic theory and statistical mechanics, regarding the compatibility and origin of random and chaotic behavior in deterministic dynamical systems. A detailed critique of some quite radical proposals of the Prigogine school is given. I argue that their conclusion regarding the conceptual bankruptcy of the classical conceptions of an exact microstate and unique phase space trajectory is not completely justified. The analogy they want to draw with quantum mechanics is not sufficiently close to support their most radical conclusion.

Type
Research Article
Information
Philosophy of Science , Volume 58 , Issue 2 , June 1991 , pp. 241 - 263
Copyright
Copyright © 1991 The Philosophy of Science Association

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Footnotes

†

I would like to thank Larry Sklar, Mark Wilson, and Tim McCarthy for valuable comments and advice.

References

Arnold, V. I. and Avez, A. (1968), Ergodic Problems of Classical Mechanics. New York: Benjamin Press.Google Scholar
Batterman, R. W. (1990), “Irreversibility and Statistical Mechanics: A New Approach?”, Philosophy of Science 57: 395–419.CrossRefGoogle Scholar
Courbage, M. (1983), “Intrinsic Irreversibility of Kolmogorov Dynamical Systems”, Physica A 122A: 459–482.CrossRefGoogle Scholar
Courbage, M. and Misra, B. (1980), “On the Equivalence Between Bernoulli Dynamical Systems and Stochastic Markov Processes”, Physica A 104A: 359–377.CrossRefGoogle Scholar
Earman, J. (1986), A Primer on Determinism. Dordrecht: Reidel.CrossRefGoogle Scholar
Ehrenfest, P. and Ehrenfest, T. (1959), The Conceptual Foundations of the Statistical Approach in Mechanics. Translated by Moravesik, M. J. Ithaca: Cornell University Press.Google Scholar
Goldstein, S.; Misra, B.; and Courbage, M. (1981), “On Intrinsic Randomness of Dynamical Systems”, Journal of Statistical Physics 25: 111–126.CrossRefGoogle Scholar
Goodrich, K.; Gustafson, K.; and Misra, B. (1980), “On Converse to Koopman's Lemma”, Physica A 102A: 379–388.CrossRefGoogle Scholar
Koopman, B. O. (1931), “Hamiltonian Systems and Transformations in Hilbert Space”, Proceedings of the National Academy of the Sciences of the United States of America 17: 315–318.Google Scholar
Krylov, N. S. (1979), Works on the Foundations of Statistical Physics. Translated by Migdal, A. B.; Sinai, Ya. G.; and Zeeman, Yu. L. Princeton: Princeton University Press.Google Scholar
Lanford, O. E. (1983), “On a Derivation of the Boltzmann Equation”, in J. L. Lebowitz and E. W. Montroll (eds.), Nonequilibrium Phenomena 1: The Boltzmann Equation. Amsterdam: North-Holland, pp. 1–17.Google Scholar
Lebowitz, J. L. (1981), “Microscopic Dynamics and Macroscopic Laws”, in C. W. Horton, L. E. Reichl, and V. G. Szebehely (eds.), Proceedings of the Workshop on Long-Time Predictions in Nonlinear Conservative Dynamical Systems. New York: Wiley & Sons, pp. 3–19.Google Scholar
Malament, D. and Zabell, S. (1980), “Why Gibbs Phase Averages Work—The Role of Ergodic Theory”, Philosophy of Science 47: 339–349.CrossRefGoogle Scholar
Misra, B. and Prigogine, I. (1980), “On the Foundations of Kinetic Theory”, Supplement of the Progress of Theoretical Physics, No. 69: 101–110.CrossRefGoogle Scholar
Misra, B. and Prigogine, I. (1981), “Time, Probability, and Dynamics”, in C. W. Horton, L. E. Reichl, and V. G. Szebehely (eds.), Proceedings of the Workshop on Long-Time Predictions in Nonlinear Conservative Dynamical Systems. New York: Wiley & Sons, pp. 21–43.Google Scholar
Misra, B. and Prigogine, I. (1983), “Irreversibility and Nonlocality”, Letters in Mathematical Physics 7: 421–429.CrossRefGoogle Scholar
Misra, B.; Prigogine, I.; and Courbage, M. (1979), “From Deterministic Dynamics to Probabilistic Descriptions”, Physica A 98A: 1–26..CrossRefGoogle Scholar
Ornstein, D. S. (1974), Ergodic Theory, Randomness, and Dynamical Systems. New Haven: Yale University Press.Google Scholar
Reed, M. and Simon, B. (1980), Methods of Modern Mathematical Physics, 1: Functional Analysis. Orlando: Academic Press.Google Scholar
Schwartz, L. (1966), Mathematics for the Physical Sciences. Reading: Addison-Wesley.Google Scholar
Shields, P. (1973), The Theory of Bernoulli Shifts. Chicago: University of Chicago Press.Google Scholar
Sklar, L. (1973), “Statistical Explanation and Ergodic Theory”, Philosophy of Science 40: 194–212.CrossRefGoogle Scholar
Yosida, K. (1978), Functional Analysis, 5th ed. Berlin: Springer-Verlag.CrossRefGoogle Scholar