Fine-grained and coarse-grained entropy in problems of statistical mechanics
- 123 Downloads
We consider dynamical systems with a phase space Γ that preserve a measure μ. A partition of Γ into parts of finite μ-measure generates the coarse-grained entropy, a functional that is defined on the space of probability measures on Γ and generalizes the usual (ordinary or fine-grained) Gibbs entropy. We study the approximation properties of the coarse-grained entropy under refinement of the partition and also the properties of the coarse-grained entropy as a function of time.
Keywordsinvariant measure Gibbs entropy coarse-grained entropy
Unable to display preview. Download preview PDF.
- 1.R. Bowen, Methods in Symbolic Dynamics [Russian transl. of selected works], Mir, Moscow (1979).Google Scholar
- 3.N. S. Krylov, Works on the Foundations of Statistical Physics [in Russian], Izdat. Akad. Nauk SSSR, Moscow (1950); English transl., Princeton Univ. Press, Princeton, N. J. (1979).Google Scholar
- 4.H. Poincaré, Journal de Physique Théorique et Appliquée, 4 Série, 5, 369–403 (1906).Google Scholar
- 5.J. W. Gibbs, Thermodynamics: Statistical Mechanics [Russian transl. of selected works], Nauka, Moscow (1982).Google Scholar
- 8.S. V. Goncharenko, D. V. Turaev, and L. P. Shil’nikov, Dokl. Rossiiskoi Akad. Nauk, 407, 299–303 (2006).Google Scholar