Revisiting the thermostatistics of the Grüneisen parameters and applications to quasiharmonic solids

•Exact thermodynamic relations between various types of Grüneisen parameters.•Thermodynamical formulation and consequences of Grüneisen׳s rule.•Thermostatistical treatment of the Grüneisen parameters for quasiharmonic solids.

We present an integrated thermostatistical study of the Grüneisen parameter and its application to a quasiharmonic solid. This analysis comprises two parts. The first part considers the connections between different thermodynamic formulations of the Grüneisen parameter, including those arising from the Mie-Grüneisen formula and related equations of state. We also establish the most general consequences of the so-called Grüneisen׳s rule. In the second part, Grüneisen׳s rule is used to establish the thermostatistics of a solid that obeys the quasiharmonic approximation. Both cases are relevant to the application of fundamental microscopic models of the heat capacity of solids.