Thermodynamics of supercooled liquids in the inherent-structure formalism:a case study

In this article we review the thermodynamics of liquids in the framework of the inherent-structure formalism. We then present calculations of the dist ribution of the basins in the potential energy of a binary Lennard-Jones mi xture as a function of temperature. The comparison between the numerical da ta and the theoretical formalism allows us to evaluate the degeneracy of th e inherent structures in a hulk system and to estimate the energy of the lo west-energy disordered state (which we define as the Kauzmann energy). We f ind that, around the mode-coupling temperature, the partition function of t he liquid is approximated well by the product of two loosely coupled partit ion functions, one depending on the inherent-structure quantities (depths o f the basins and their degeneracy) and one describing the free energy of th e liquid constrained in one typical basin.