Amoebas of complex hypersurfaces in statistical thermodynamics

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.Comment: 18 pages, 5 figure

On the Asymptotics of the Vector Partition Function

Используя методы теории производящих функций и интегральных представлений, получена асимптотическая оценка для функции векторного разбиения.We obtain the asymptotic estimate for the vector partition function by using generating functions and the integral representations method

On the Asymptotics of the Vector Partition Function

Используя методы теории производящих функций и интегральных представлений, получена асимптотическая оценка для функции векторного разбиения.We obtain the asymptotic estimate for the vector partition function by using generating functions and the integral representations method