Amoebas of complex hypersurfaces in statistical thermodynamics

Abstract

The amoeba of a complex hypersurface is its image under a logarithmic projection. A number of properties of algebraic hypersurface amoebas are carried over to the case of transcendental hypersurfaces. We demonstrate the potential that amoebas can bring into statistical physics by considering the problem of energy distribution in a quantum thermodynamic ensemble. The spectrum ${\epsilon }_k\subset {\mathbb{Z}}^n$ of the ensemble is assumed to be multidimensional; this leads us to the notions of a multidimensional temperature and a vector of differential thermodynamic forms. Strictly speaking, in the paper we develop the multidimensional Darwin and Fowler method and give the description of the domain of admissible average values of energy for which the thermodynamic limit exists.

18 pages, 5 figures

References in corpus (1)

• Thermodynamics and the moment map

Cited by in corpus (7)

• Kinematic singularities of Feynman integrals and principal A-determinants
• Geometry of the basic statistical physics mapping
• The Boundary of Amoebas
• Signatures of partition functions and their complexity reduction through the KP II equation
• Zeros and amoebas of partition functions
• Trigonometric Convexity for the Multidimensional Indicator after Ivanov
• Degenerations of amoebae and Berkovich spaces