Energy landscapes, ideal glasses, and their equation of state

TL;DR

This paper extends the inherent structure formalism to describe the thermodynamics and equation of state of systems with an ideal glass transition, linking landscape properties to simulation data and the Sastry density.

Contribution

It generalizes the landscape-based thermodynamics to include an ideal glass transition and develops a simple model matching simulation data for Lennard-Jones fluids.

Findings

Separation of configurational and vibrational pressure contributions.

Accurate equation of state for Lennard-Jones fluid.

Connection between landscape properties and Sastry density.

Abstract

Using the inherent structure formalism originally proposed by Stillinger and Weber [Phys. Rev. A 25, 978 (1982)], we generalize the thermodynamics of an energy landscape that has an ideal glass transition and derive the consequences for its equation of state. In doing so, we identify a separation of configurational and vibrational contributions to the pressure that corresponds with simulation studies performed in the inherent structure formalism. We develop an elementary model of landscapes appropriate to simple liquids which is based on the scaling properties of the soft-sphere potential complemented with a mean-field attraction. The resulting equation of state provides an accurate representation of simulation data for the Lennard-Jones fluid, suggesting the usefulness of a landscape-based formulation of supercooled liquid thermodynamics. Finally, we consider the implications of both the general theory and the model with respect to the so-called Sastry density and the ideal glass transition. Our analysis shows that a quantitative connection can be made between properties of the landscape and a simulation-determined Sastry density, and it emphasizes the distinction between an ideal glass transition and a Kauzmann equal-entropy condition.