A study is made of the thermodynamics of a non-local medium whose evolution is governed not only by the temperature and pressure, but also by the field of a relaxation parameter. For solid-state materials which undergo a phase transition, such a relaxation parameter is the order parameter. Heat transport equations are derived together with a thermodynamic inequality which must be satisfied during relaxation. The motion of an interphase boundary during a first-order phase transition is investigated. It is shown that, if the width of the boundary exceeds a critical value, there are steady-state conditions under which the new phase formed in an exothermal transition may be at a temperature above the equilibrium temperature
