High temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions on a sphere and cylinder

TL;DR

This paper develops a universal method to derive high temperature asymptotics of thermodynamic functions for electromagnetic fields with spherical and cylindrical boundary conditions, involving new heat kernel coefficients.

Contribution

It introduces a general expansion approach using heat kernel coefficients, including newly calculated terms, applicable to various boundary value problems.

Findings

Reproduces known asymptotics for electromagnetic fields with boundary conditions

Includes new terms in high temperature expansions

Demonstrates universality of the method for different boundary problems

Abstract

The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel coefficients and the related determinant. For this, some new heat kernel coefficients and determinants had to be calculated for the boundary conditions under consideration. The obtained results reproduce all the asymptotics derived by other methods in the problems at hand and involve a few new terms in the high temperature expansions. An obvious merit of this approach is its universality and applicability to any boundary value problem correctly formulated.