Geodesic
Fine-grained and coarse-grained entropy in problems of statistical mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 120-137

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We consider dynamical systems with a phase space $\Gamma$ that preserve a measure $\mu$. A partition of $\Gamma$ into parts of finite $\mu$-measure generates the coarse-grained entropy, a functional that is defined on the space of probability measures on $\Gamma$ 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.
Keywords: invariant measure, Gibbs entropy, coarse-grained entropy. 
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     author = {V. V. Kozlov and D. V. Treschev},
     title = {Fine-grained and coarse-grained entropy in problems of statistical mechanics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_151_1_a7/}
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V. V. Kozlov; D. V. Treschev. Fine-grained and coarse-grained entropy in problems of statistical mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 120-137. http://geodesic.mathdoc.fr/item/TMF_2007_151_1_a7/