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 distribution of the basins in the potential energy of a binary Lennard-Jones mixture as a function of temperature. The comparison between the numerical data and the theoretical formalism allows us to evaluate the degeneracy of the inherent structures in a bulk system and to estimate the energy of the lowest-energy disordered state (which we define as the Kauzmann energy). We find that, around the mode-coupling temperature, the partition function of the liquid is approximated well by the product of two loosely coupled partition functions, one depending on the inherent-structure quantities (depths of the basins and their degeneracy) and one describing the free energy of the liquid constrained in one typical basin.