Configurational entropy of polydisperse systems can never reach zero

TL;DR

This paper shows that the configurational entropy of polydisperse systems cannot reach zero and is bounded below by the entropy of mixing, with implications for theories of glass transition.

Contribution

It demonstrates that configurational entropy in polydisperse systems is inherently limited by mixing entropy, affecting theoretical models like Adam-Gibbs and RFOT.

Findings

Configurational entropy cannot reach zero in polydisperse systems.

The lower bound of entropy is given by the entropy of mixing.

Results align with recent free energy landscape studies.

Abstract

We present examples of systems whose configurational entropy $S_{\text{conf}}$ can never reach zero and is instead limited from below by the entropy of mixing $S_{\text{mix}}$ of the corresponding ideal gas. We use $S_{\text{conf}}$ defined through the local minima of the potential energy landscape, $S_{\text{conf}}^{\text{PEL}}$. We show that this happens in mean-field models, in collections of hard spheres with infinitesimal polydispersity, and for one-dimensional hard rods. We demonstrate that these results match recent advances in understanding the configurational entropy defined in the free energy landscape, $S_{\text{conf}}^{\text{FEL}}$. We demonstrate that if $\min( S_{\text{conf}}^{\text{FEL}} ) = 0$, then for an arbitrary system $\min( S_{\text{conf}}^{\text{PEL}} ) = A N + S_{\text{mix}}$, where $N$ is the number of particles and $A$ is some constant determined by the interaction potential. We discuss which implications these results have on the Adam--Gibbs (AG) and RFOT relations and show that the latter retain a physically meaningful shape for both configurational entropies, $S_{\text{conf}}^{\text{FEL}}$ and $S_{\text{conf}}^{\text{PEL}}$.