Geometry of the basic statistical physics mapping

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.

28 pages

References in corpus (5)

• Classification of the line-soliton solutions of KPII
• Phase transitions in geometrothermodynamics
• Contact Symmetries and Hamiltonian Thermodynamics
• Geometric thermodynamics: black holes and the meaning of the scalar curvature
• Tropical Limit in Statistical Physics

Cited by in corpus (4)

• Tropical limit and the micro-macro correspondence
• Entropy driven transformations of statistical hypersurfaces
• Signatures of partition functions and their complexity reduction through the KP II equation
• Zeros and amoebas of partition functions