Description of thermal conductivity in the Ginzburg-Landau theory of phase transitions

Abstract

A generalization of the Ginzburg-Landau theory of phase transitions is presented which allows one to describe states with variable temperatures. The approach is based on an expression for the entropy in the form of a functional which depends on the temperature gradient and the order parameter. It is shown that the theory is compatible with the zero-th law of thermodynamics (constancy of the temperature in equilibrium). For equilibrium thermodynamically stable states the results of the theory agree with the results of the isothermal approach based on the free energy functional. General limitations on the possible form of the nonlinear dynamic equations are given, in particular for the heat flux vector, and possible particular versions are given. The dynamics of linear fluctuations has been included, including temperature fluctuations.