On a phenomenological non-equilibrium entropy for a class of rigid heat conductors

From a semi-empirical model for the relaxation time of the heat flux and from a generalised Maxwell relation, we obtain the equations of state of an extended Gibbs equation which describes the dependence of a non-equilibrium entropy on the internal energy and the heat flux. By integration of the Gibbs equation, we obtain an explicit expression for the corresponding non-equilibrium entropy. © 1981 The Institute of Physics.