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.