Information and configurational entropy in glassy systems

Abstract It is often claimed that snapshots of molecular positions in a glass and a liquid appear indistinguishable. However, we argue that given multiple snapshots taken over a time interval, there exists a well-defined procedure to quantify the degree of glassiness in a given system as it evolves. By concatenating these snapshots and applying a lossless compression protocol, one can extract meaningful structural information: We propose that the size of the (losslessly) compressed file provides a direct first-principle measure of both ‘vibrational’ and ‘configurational’ per particle entropies. The information shared by configurations over long timescales thus provides a natural definition of ‘configurational entropy,’ a concept fundamental to our understanding of glasses. Furthermore, this method naturally introduces an associated glass length scale, both in and out of equilibrium, through the size and frequency of repeated motifs essential for compression - a quantity that would diverge at a putative glass transition. The approach remains agnostic to any specific theoretical framework, independent of the nature of the constituents, and relies only on the existence of a timescale significantly slower than the microscopic one.