Microscopic Theory of Irreversible Processes

• Published in: Proceedings of the National Academy of Sciences - PNAS 1977-10, Vol.74 (10), p.4152-4156
• Main Authors: Prigogine, I., Mayné, F., George, C., De Haan, M.
• Format: Article
• Language: English
• Subjects: Continuous spectra; Distribution functions; Entropy; Liouville equations; Mathematical functions; Physical Sciences: Physics; Physics; Quantum mechanics; Thermodynamic irreversibility; Thermodynamics; Time dependence
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.74.10.4152

The microscopic theory of irreversible processes that we developed is summarized and illustrated, using as a simple example the Friedrichs model. Our approach combines the Poincaré's point of view (dynamical interpretation of irreversibility) with the Gibbs-Einstein ensemble point of view. It essentially consists in a nonunitary transformation theory based on the symmetry properties of the Liouville equation and dealing with continuous spectrum. The second law acquires a microscopic content in terms of a Liapounov function which is a quadratic functional of the density operator. In our new representation of dynamics, which is defined for a restricted set of observables and states, this functional takes a universal form. We obtain, in this way, a semi-group description, the generator of which contains a part directly related to the microscopic entropy production. The Friedrichs model gives us a simple field theoretical example for which the entropy production can be evaluated. The thermodynamical meaning of life-times is explicitly displayed. The transition from pure states to mixtures, as well as the occurrence of long tails in thermo-dynamic systems, are also briefly discussed.