Collective Variables and Dissipation
This course is an introduction to some basic concepts of non-equilibrium statistical mechanics. We emphasize in particular the relevant entropy relative to a given set of collective variables, the meaning of the projection method in the Liouville space, its use to establish the generalized transport equations for these variables, and the interpretation of dissipation in the framework of information theory.
KeywordsDensity Operator Liouville Equation Statistical Entropy Liouville Operator Liouville Representation
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- 1.R. Balian, Y. Alhassid et H. Reinhardt, Physics Reports, in preparation. This article treats with more details most of the themes presented here, and includes a bibliography.Google Scholar
- 2.The projection method underlies many articles, quoted in the books of F. Haake, Statistical treatment of open systems by generalized master equations, Springer Tracts in Modern Physics, vol. 66 (Berlin, 1973) and of H. Grabert, Projection31 operator techniques in non equilibrium statistical mechanics, Springer tracts,vol. 95 (Berlin, 1982), as well as in the review article of O. Penrose, Rep. on Progress in Phys. 42 (1979) 1937. It has been introduced by S. Nakajima, Progr. Theor.Phys. 20 (1958) 948, by R. Zwanzig, J.Chem.Phys. 33 (1960) 1338; Physica 30 (1964) 1109, and by H. Mori and K. Kawasaki, Progr.Theor.Phys. 27 (1962) 529. Its metric interpretation is given in ref. 1.Google Scholar