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We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…

Statistical Mechanics · Physics 2025-12-03 Dallin Fisher , Qi-Jun Hong

We review a statistical picture of the glassy state derived from the analysis of the off-equilibrium fluctuation-dissipation relations. We define an ultra-long time limit where ``one time quantities'' are close to equilibrium while response…

Statistical Mechanics · Physics 2009-11-07 Silvio Franz

The conventional approach to study glasses either requires considering the rapid drop in the excess entropy {\Delta}S_ex or the free volume V_f. As the two quantities are not directly related to each other, the viscosity in the two…

Statistical Mechanics · Physics 2018-02-27 P. D. Gujrati

The rigid to floppy transitions and the associated intermediate phase in glasses are studied in the case where the local structure is not fully determined from the macroscopic concentration. The approach uses size increasing cluster…

Disordered Systems and Neural Networks · Physics 2009-11-11 Matthieu Micoulaut

Supercooled liquids are sometimes described as being composed of a mosaic of patches that may be listed in a `library', each one having some form of non-periodic order. Looking closer, one finds this construction elusive. In attempting to…

Statistical Mechanics · Physics 2024-06-25 Jorge Kurchan

Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…

Probability · Mathematics 2026-05-29 Joseph Samuel Miller

Collective behavior, both in real biological systems as well as in theoretical models, often displays a rich combination of different kinds of order. A clear-cut and unique definition of "phase" based on the standard concept of order…

Statistical Mechanics · Physics 2021-06-30 Andrea Cavagna , Paul M. Chaikin , Dov Levine , Stefano Martiniani , Andrea Puglisi , Massimiliano Viale

Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…

Data Structures and Algorithms · Computer Science 2020-11-17 Michel Schellekens

We introduce a new quantity to probe the glass transition. This quantity is a linear generalized compressibility which depends solely on the positions of the particles. We have performed a molecular dynamics simulation on a glass forming…

Disordered Systems and Neural Networks · Physics 2009-11-07 Herve M. Carruzzo , Clare C. Yu

Several papers have recently presented results of measurements of physical aging by studying the behavior of glassy materials quenched from temperatures above their glass transition temperature $T_g$. The evolution of the aging process is…

Materials Science · Physics 2017-04-26 Vassiliki Katsika-Tsigourakou , Georgios E. Zardas

In this talk we discuss the possibility of constructing a fluctuation theory for structural glasses in the non-equilibrium aging state. After reviewing well known results in a toy model we discuss some of the key assumptions which support…

Disordered Systems and Neural Networks · Physics 2009-10-31 Andrea Crisanti , Felix Ritort

Glassiness occurs when disorder and frustration cause local degrees of freedom to freeze despite the lack of long-range order. In systems of interacting bosons, such glassiness may involve a purely quantum degree of…

Disordered Systems and Neural Networks · Physics 2026-03-24 Anna M. Piekarska , Tadeusz K. Kopeć

We propose that chaotic Glass networks (a class of piecewise-linear Ordinary Differential Equations) are good candidates for the design of true random number generators. A Glass network design has the advantage of involving only standard…

Dynamical Systems · Mathematics 2025-02-14 Benjamin W. Wild , Roderick Edwards

We review an scenario for the non-equilibrium dynamics of glassy systems that has been motivated by the exact solution of simple models. This approach allows one to set on firmer grounds well-known phenomenological theories. The old ideas…

Statistical Mechanics · Physics 2009-11-07 Leticia F. Cugliandolo

We show in numerical simulations that a system of two coupled replicas of a binary mixture of hard spheres undergoes a phase transition in equilibrium at a density slightly smaller than the glass transition density for an unreplicated…

Disordered Systems and Neural Networks · Physics 2014-03-03 G. Parisi , B. Seoane

We study the low temperature dynamics of a two dimensional short-range spin system with uniform ferromagnetic interactions, which displays glassiness at low temperatures despite the absence of disorder or frustration. The model has a dual…

Disordered Systems and Neural Networks · Physics 2009-10-31 Juan P. Garrahan , M. E. J. Newman

We present evidence from computer simulations for glassy dynamics in suspensions of monodisperse hard ellipsoids. In equilibrium, almost spherical ellipsoids show a first order transition from an isotropic phase to a rotator phase. When…

Soft Condensed Matter · Physics 2008-09-18 Patrick Pfleiderer , Kristina Milinkovic , Tanja Schilling

In an effort to understand the glass transition, the dynamics of a non-randomly frustrated spin model has been analyzed. The phenomenology of the spin model is similar to that of a supercooled liquid undergoing the glass transition. The…

Statistical Mechanics · Physics 2009-10-31 Hui Yin , Bulbul Chakraborty

Ordering at arbitrarily high temperature - entropic order - has been argued to take place in a class of generalized Ising models parameterised by a real interaction parameter $p$ when $p\ge 1$. We give a rigorous proof of this conjecture.…

Statistical Mechanics · Physics 2026-04-14 Enrico Andriolo , Mendel Nguyen , Emily Richards , Tin Sulejmanpasic

A system is glassy when the observation time is much smaller than the equilibration time. A unifying thermodynamic picture of the glassy state is presented. Slow configurational modes are in quasi-equilibrium at an effective temperature. It…

Statistical Mechanics · Physics 2009-10-31 Th. M. Nieuwenhuizen