Configurational entropy of polydisperse systems can never reach zero

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 $\min (S_{\text{conf}}^{\text{PEL}})=AN+S_{\text{mix}}$, 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 $S_{\text{conf}}^{\text{PEL}}$.

The paper is not scientifically sound and makes several unjustified assumptions. The examples that are sound are unfortunately almost trivial. We did not find a reasonable way to fix or alleviate these problems. These deficiencies were pointed out by several independent reviewers during a peer-review process