# Effect of particle exchange on the glass transition of binary hard spheres

## TL;DR

This paper explores how allowing or prohibiting particle exchange in binary hard sphere glasses affects the predicted glass transition points, with implications for understanding relaxation dynamics and entropy estimation.

## Contribution

It introduces and compares two ans"atze for the replica theory of binary hard sphere glasses, highlighting the impact of particle exchange on transition densities.

## Key findings

- Dynamical transition density is lower with exchange allowed.
- Thermodynamical transition density is higher with exchange allowed.
- Particle exchange influences relaxation times and entropy estimates.

## Abstract

We investigate the replica theory of the liquid-glass transition for a binary mixture of large and small additive hard spheres. We consider two different ans\"atze for this problem: the frozen glass ansatz (FGA) in whichs the exchange of large and small particles in a glass state is prohibited, and the exchange glass ansatz (EGA), in which it is allowed. We calculate the dynamical and thermodynamical glass transition points with the two ans\"atze. We show that the dynamical transition density of the FGA is lower than that of the EGA, while the thermodynamical transition density of the FGA is higher than that of the EGA. We discuss the algorithmic implications of these results for the density-dependence of the relaxation time of supercooled liquids. We particularly emphasize the difference between the standard Monte Carlo and swap Monte Carlo algorithms. Furthermore, we discuss the importance of particle exchange for estimating the configurational entropy.