Geometric study for the Legendre duality of generalized entropies and its application to the porous medium equation

Details Geometric study for the Legendre duality of generalized entropies and its application to the porous medium equation Geometric study for the Legendre duality of generalized entropies and its application to the porous medium equation

2009-04-09

arxiv.org/abs/0904.1530v1

Physics

Condensed Matter

Statistical Mechanics

Invited contribution to the SigmaPhi 2008 Conference

Scientific paper

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 a behavior of the solution to the nonlinear diffusion equation called the {\em porous medium equation}.

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