An alternative, dynamic density functional-like theory for time-dependent density fluctuations in glass-forming fluids

TL;DR

This paper introduces a new local-in-time dynamic density functional-like theory for understanding density fluctuations and dynamic arrest in glass-forming fluids, linking static free energy landscapes to dynamic transitions.

Contribution

It develops an alternative, local-in-time equation of motion for density fluctuations that connects static free energy minima to dynamic arrest phenomena in glasses.

Findings

The theory predicts a dynamic arrest when a local minimum of the free energy appears.

It aligns the ergodicity breaking transition with the static transition from the free energy landscape.

The approach offers a new perspective on glass transition dynamics.

Abstract

We propose an alternative theory for the relaxation of density fluctuations in glass-forming fluids. We derive an equation of motion for the density correlation function which is local in time and is similar in spirit to the equation of motion for the average non-uniform density profile derived within the dynamic density functional theory. We identify the Franz-Parisi free energy functional as the non-equilibrium free energy for the evolution of the density correlation function. An appearance of a local minimum of this functional leads to a dynamic arrest. Thus, the ergodicity breaking transition predicted by our theory coincides with the dynamic transition of the static approach based on the same non-equilibrium free energy functional.