Coarse Graining, Nonmaximal Entropy, and Power Laws
| Autor: | Ian L. Pegg, Fernando C. Pérez-Cárdenas, Lorenzo Resca |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
Principle of maximum entropy General Physics and Astronomy lcsh:Astrophysics 01 natural sciences Power law lcsh:QC1-999 Article 010305 fluids & plasmas coarse graining 0103 physical sciences Thermodynamic limit lcsh:QB460-466 nonmaximal entropy lcsh:Q Granularity Statistical physics 010306 general physics lcsh:Science entropy power laws lcsh:Physics |
| Zdroj: | Entropy Volume 20 Issue 10 Entropy, Vol 20, Iss 10, p 737 (2018) |
| ISSN: | 1099-4300 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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