Open AccessMicroscopic theory of irreversible processes
Author(s) -
Ilya Prigogine,
Fernand Mayne,
Claude George,
Michel De Haan
Publication year - 1977
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.74.10.4152
Subject(s) - observable , statistical physics , entropy production , operator (biology) , microscopic theory , simple (philosophy) , entropy (arrow of time) , generator (circuit theory) , physics , interpretation (philosophy) , quadratic equation , theoretical physics , mathematics , thermodynamics , quantum mechanics , computer science , chemistry , biochemistry , philosophy , power (physics) , geometry , epistemology , repressor , transcription factor , gene , programming language
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 thermodynamic systems, are also briefly discussed.