Geometric study for the Legendre duality of generalized entropies and its application to the porous medium equation |
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Authors: | A Ohara |
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Institution: | (1) Department of Systems Science, Osaka University, 1-3 Machikane-yama, Toyonaka, 560-8531 Osaka, Japan |
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Abstract: | We geometrically study the Legendre duality relation that plays an important role in statistical physics with the standard
or generalized entropies. For this purpose, we introduce dualistic structure defined by information geometry, and discuss
concepts arising in generalized thermostatistics, such as relative entropies, escort distributions and modified expectations.
Further, a possible generalization of these concepts in a certain direction is also considered.
Finally, as an application of such a geometric viewpoint, we briefly demonstrate several new results on the behavior of the
solution to a nonlinear diffusion equation called the porous medium equation. |
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Keywords: | PACS" target="_blank">PACS 89 70 Cf Entropy and other measures of information 02 40 Hw Classical differential geometry 05 90 +m Other topics in statistical physics thermodynamics and nonlinear dynamical systems |
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