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The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

General Topology · Mathematics 2013-08-20 Dikran Dikranjan , Anna Giordano Bruno

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…

Statistical Mechanics · Physics 2020-05-11 S. E. Marzen , J. P. Crutchfield

We numerically calculate the configurational entropy S_conf of a binary mixture of hard spheres, by using a perturbed Hamiltonian method trapping the system inside a given state, which requires less assumptions than the previous methods…

Disordered Systems and Neural Networks · Physics 2015-06-25 L. Angelani , G. Foffi

We extend the notion of the geometric entropy of foliation to foliated manifolds equipped with leafwise Finsler structure. We study the relation between the geometric entropy and the topological entropy of the holonomy pseudogroup. The case…

Differential Geometry · Mathematics 2015-01-30 Ilona Michalik , Szymon M. Walczak

We investigate numerically the identification of relevant structural features that contribute to the dynamical heterogeneity in a model glass-forming liquid. By employing the recently proposed information imbalance technique, we select…

Soft Condensed Matter · Physics 2024-11-14 Anand Sharma , Chen Liu , Misaki Ozawa

We propose a microscopic model without energy barriers in order to explain some generic features observed in structural glasses. The statics can be exactly solved while the dynamics has been clarified using Monte Carlo calculations.…

Condensed Matter · Physics 2009-10-28 Felix Ritort

We provide a perspective on polymer glass formation, with an emphasis on models in which the fluid entropy and collective particle motion dominate the theoretical description and data analysis. We first discuss the dynamics of liquids in…

Soft Condensed Matter · Physics 2021-02-25 Wen-Sheng Xu , Jack F. Douglas , Zhao-Yan Sun

We highlight certain key achievements in experimental work on molecular, colloidal and granular glassformers. This short review considers these three classes of experimental systems and focusses largely on the work of the authors and their…

Soft Condensed Matter · Physics 2023-10-16 Olivier Dauchot , François Ladieu , C. Patrick Royall

Around a glass transition, the dynamics of a supercooled liquid dramatically slow down, exhibited by caging of particles, while the structural changes remain subtle. In alternative to recent machine learning studies searching for structural…

Disordered Systems and Neural Networks · Physics 2022-09-07 Kaihua Zhang , Xinyang Li , Yuliang Jin , Ying Jiang

Active matter, whose motion is driven, and glasses, whose dynamics are arrested, seem to lie at opposite ends of the spectrum in nonequilibrium systems. In spite of this, both classes of systems exhibit a multitude of stable states that are…

Statistical Mechanics · Physics 2014-06-10 K. R. Pilkiewicz , J. D. Eaves

This Ph.D. thesis is divided in two parts. The first one concerns the equilibrium properties of glassy systems. Some aspects of the phenomenology of glasses and of theories attempting to describe them are reviewed in chapter 1. A study of…

Disordered Systems and Neural Networks · Physics 2007-05-23 F. Zamponi

The ground state dynamics of an entropy barrier model proposed recently for describing relaxation of glassy systems is considered. At stages of evolution the dynamics can be described by a simple variant of the Ehrenfest urn model.…

Statistical Mechanics · Physics 2009-10-30 K. P. N. Murthy , K. W. Kehr

We summarize a theoretical framework based on global time-reparametrization invariance that explains the origin of dynamic fluctuations in glassy systems. We introduce the main ideas without getting into much technical details. We describe…

Disordered Systems and Neural Networks · Physics 2009-11-13 Claudio Chamon , Leticia F. Cugliandolo

We use machine learning methods on local structure to identify flow defects - or regions susceptible to rearrangement - in jammed and glassy systems. We apply this method successfully to two disparate systems: a two dimensional experimental…

Spin-glasses are universal models that can capture complex behavior of many-body systems at the interface of statistical physics and computer science including discrete optimization, inference in graphical models, and automated reasoning.…

Machine Learning · Computer Science 2020-01-14 Gavin S. Hartnett , Masoud Mohseni

Slow conductance relaxations are observable in a many condensed matter systems. These are sometimes described as manifestations of a glassy phase. The underlying mechanisms responsible for the slow dynamics are often due to structural…

Disordered Systems and Neural Networks · Physics 2008-11-21 Z. Ovadyahu

Typical properties of glassy materials are shown to be captured by a mean-field free-volume theory. Relaxation processes are supposed to be free-volume activated, and different entropy barriers are associated with density relaxation and…

Condensed Matter · Physics 2016-08-16 Anaël Lemaître

Understanding glass formation by quenching remains a challenge in soft condensed matter physics. Recent numerical studies on steepest descent dynamics, which is one of the simplest models of quenching, revealed that quenched liquids undergo…

Soft Condensed Matter · Physics 2024-01-29 Masanari Shimada , Kumpei Shiraishi , Hideyuki Mizuno , Atsushi Ikeda

In this paper we review a recent proposal to understand the long time limit of glassy dynamics in terms of an appropriate Markov Chain. [1]. The advantages of the resulting construction are many. The first one is that it gives a quasi…

Disordered Systems and Neural Networks · Physics 2016-04-19 Silvio Franz , Giorgio Parisi , Federico Ricci-Tersenghi , Pierfrancesco Urbani

We use computer simulations to probe the thermodynamic and dynamic properties of a glass-former that undergoes an ideal glass-transition because of the presence of randomly pinned particles. We find that even deep in the equilibrium glass…

Disordered Systems and Neural Networks · Physics 2018-12-03 Misaki Ozawa , Atsushi Ikeda , Kunimasa Miyazaki , Walter Kob
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