Geometry of the basic statistical physics mapping
Mathematical Physics
2016-09-21 v1 Statistical Mechanics
Differential Geometry
math.MP
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.
Cite
@article{arxiv.1602.07931,
title = {Geometry of the basic statistical physics mapping},
author = {Mario Angelelli and Boris Konopelchenko},
journal= {arXiv preprint arXiv:1602.07931},
year = {2016}
}
Comments
28 pages