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Fine-grained and coarse-grained entropy in problems of statistical mechanics. (English. Russian original) Zbl 1119.82005
Theor. Math. Phys. 151, No. 1, 539-555 (2007); translation from Teor. Mat. Fiz. 151, No. 1, 120-137 (2007).
The paper deals with a so-called “coarse-grained entropy” which is exactly the informational “weighted entropy” introduced in the literature a few decades ago by some scientists in information theory [see S. Guiaşu, Rep. Math. Phys. 2, 165–179 (1971; Zbl 0222.62004)]. Perhaps its main contribution is to clarify the practical meaning of this entropy in physics. For instance, it is shown that it does not necessarily increase in time as it was believed by eminent scientists. Also, one analyzes its behaviour when the “thickness” of the coarse-graining effect tends to zero.

82B05 Classical equilibrium statistical mechanics (general)
62B10 Statistical aspects of information-theoretic topics
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