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Keywords = nonmaximal entropy

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Article
Coarse Graining, Nonmaximal Entropy, and Power Laws
by Fernando C. Pérez-Cárdenas, Lorenzo Resca and Ian L. Pegg
Entropy 2018, 20(10), 737; https://doi.org/10.3390/e20100737 - 26 Sep 2018
Cited by 5 | Viewed by 4223
Abstract
We show that coarse graining produces significant and predictable effects on the entropy of states of equilibrium when the scale of coarse graining becomes comparable to that of density fluctuations. We demonstrate that a coarse-grained entropy typically evolves toward a state of effective [...] Read more.
We show that coarse graining produces significant and predictable effects on the entropy of states of equilibrium when the scale of coarse graining becomes comparable to that of density fluctuations. We demonstrate that a coarse-grained entropy typically evolves toward a state of effective equilibrium with a lower value than that of the state of maximum entropy theoretically possible. The finer the coarse graining, the greater the drop in effective entropy, and the more relevant the fluctuations around that. Fundamental considerations allow us to derive a remarkable power law that relates coarse graining to the effective entropy gap. Another power law is found that precisely relates the noise range of effective entropy fluctuations to coarse graining. We test both power laws with numerical simulations based on a well-studied two-dimensional lattice gas model. As expected, the effects of these power laws diminish as our description approaches a macroscopic level, eventually disappearing in the thermodynamic limit, where the maximum entropy principle is reasserted. Full article
(This article belongs to the Section Statistical Physics)
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