Thermodynamics of anisotropie solids near absolute zero

A thermodynamic theory of thermoelastic bodies at cryogenic temperatures is developed in the framework of a gradient generalization of thermodynamics with internal state variables. Compatibility of model equations with second law of thermodynamics is investigated. Finally, the corresponding theory for rigid bodies, developed in a series of papers by Kosiński and coworkers is obtained as a particular case of the present one.