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arXiv · 1602.07931

Geometry of the basic statistical physics mapping

Mario Angelelli·Boris Konopelchenko
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Abstract

Geometry of hypersurfaces defined by the relation which generalizes classical formula for free energy in terms of microstates is studied. Induced metric, Riemann curvature tensor, Gauss-Kronecker curvature and associated entropy are calculated. Special class of ideal statistical hypersurfaces is analyzed in details. Non-ideal hypersurfaces and their singularities similar to those of the phase transitions are considered. Tropical limit of statistical hypersurfaces and double scaling tropical limit are discussed too.

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Mario Angelelli, Boris Konopelchenko. 2016-02-25. Geometry of the basic statistical physics mapping. https://doi.org/10.1088/1751-8113%2F49%2F38%2F385202

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