Configurational entropy of polydisperse supercooled liquids

We propose a computational method to measure the configurational entropy in generic polydisperse glass-formers. In particular, our method resolves issues related to the diverging mixing entropy term due to a continuous polydispersity. The configurational entropy is measured as the difference between the well-defined fluid entropy and a more problematic glass entropy. We show that the glass entropy can be computed by a simple generalisation of the Frenkel-Ladd thermodynamic integration method, which takes into account permutations of the particle diameters. This approach automatically provides a physically meaningful mixing entropy for the glass entropy and includes contributions that are not purely vibrational. The proposed configurational entropy is thus devoid of conceptual and technical difficulties due to continuous polydispersity, while being conceptually closer, but technically simpler, than alternative free energy approaches.