Time dependent statistical thermodynamic properties of disordered solids

It is noted that glass is in non-equilibrium state on the way to the thermal equilibrium, that is, a kind of a slow relaxation process and depends on its whole thermal history. It is also known that, in the experimental way, so called the entropy of glass measured by cooling and heating shows respectively lower and upper bounds of the entropy defined by statistical thermodynamics. In this paper, we provide a new method how to generalize a relationship described by an inequality between calorimetric entropy and statistical one in a glass state, where a time dependent H function written by a non-equilibrium probability distribution plays a main role.