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Advances in Chemical Physics, Volume 135 (Special Volume in by Stuart A. Rice

By Stuart A. Rice

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Roy. , Cl. Sciences, 28. 6. I. Prigogine, Introduction to Thermodynamics of Irreversible Processes, Charles C Thomas Publishers, Springfield, IL, 1955. , 1967. Translations in Russian, Serbo-Croatian, French, Italian, and Spanish. 7. I. Prigogine (with the collaboration of V. Mathot and A. Bellemans), The Molecular Theory of Solutions, North Holland Publishers, Amsterdam, 1957. 8. I. Prigogine and R. Defay, Chemical Thermodynamics (translation by D. H. Everett of ref. LS-3), Jarrold & Sons, Norwich.

The transformed distribution function leads to a simple definition of an entropy. The members of this class will be called intrinsically stochastic dynamical systems. A few remarks will help us in understanding the importance of this result. One should first stress the fact that this proposition (when precisely formulated) has the status of a theorem, proven with the full rigor required by mathematics. Next, one should note that we have here an ‘‘existence theorem’’: The class of systems to which it applies is defined in a univocal, but abstract, nonconstructive way.

In order to 12 In this model the continuous evolution in time is replaced by successive transformations of the space on itself (‘‘mappings’’). The baker mapping consists of starting from an L : L square and stretching it in one dimension while shrinking it in the other dimension, thus forming a rectangle 2L : L=2; one then folds the latter on itself, in order to make again a square L : L. ’’ ilya prigogine: his life, his work 21 describe these systems, it is always possible to introduce a representation (actions and angles) in terms of degrees of freedom evolving independently of each other.

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