Information and Configurational Entropy in Glassy Systems

Ittai Fraenkel, Jorge Kurchan, Dov Levine
Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn)
2024-02-07 00:00:00
It is often stated that if one is presented with a snapshot of the positions of the molecules of a glass and one of a liquid, one is unable to tell the difference. Here we argue instead that given several such snapshots taken over a time-interval, even without specifying the times, there is a definite procedure to assess precisely the level of glassiness: it suffices to concatenate the snapshots side-by-side, and to subject the joint picture to a lossless compression protocol. We argue that the size of the compressed file yields a direct and unambiguous measure of the `vibrational' and `configurational' entropies, and may be used to study the associated glass length scale in or out of equilibrium through the size and frequency of the repeated motifs essential to the compression, a quantity that would diverge at a putative glass transition.
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