Thermodynamics Of The Glassy State

In the past thirty years, the area of spin glasses has experienced rapid growth, including the development of solvable models for glassy systems. Yet these developments have only been recorded in the original research papers, rather than in a single source. 'Thermodynamics of the Glassy State' presents a comprehensive account of the modern theory of glasses, starting from basic principles (thermodynamics) to the experimental analysis of one of the most important consequences of thermodynamics-Maxwell relations.After a brief introduction to general theoretical concepts and historical developments, the book thoroughly describes glassy phenomenology and the established theory. The core of the book surveys the crucial technique of two-temperature thermodynamics, explains the success of this method in resolving previously paradoxical problems in glasses, and presents exactly solvable models, a physically realistic approach to dynamics with advantages over more established mean field methods.The authors also tackle the potential energy landscape approach and discuss more detailed theories of glassy states, including mode coupling, avoided critical point, replica, and random first order transition theories. This reference lucidly explores recent theoretical advances in the thermodynamics of slowing-aging (glassy) systems. It details the general properties of glassy states while also demonstrating how these properties are present in specific models, enabling readers to thoroughly understand this fundamental yet challenging area of study. Table of Contents: INTRODUCTION THEORY AND PHENOMENOLOGY OF GLASSES Processes, time-scales, and transitions Strong and fragile glass formers Aging Configurational entropy Adam-Gibbs entropic theory Fragility index Kovacs effect TWO TEMPERATURE THERMODYNAMICS Elements of thermodynamics Fictive temperature Two temperature thermodynamics Laws of thermodynamics for off-equilibrium systems Laws of thermodynamics for glassy magnets Effective temperature in thermal cycles Fluctuation formula and effective temperatures Fluctuation and dissipation out of equilibrium Direct measure of the effective temperature Asymptotic solution in nonlinear cooling EXACTLY SOLVABLE MODELS FOR THE GLASSY STATE Harmonic oscillator model Kinetic models with separation of timescales Out-of-equilibrium thermodynamics Below the Kauzmann transition Kovacs effect: limits of two temperature thermodynamics Measuring effective temperature in HO models Mode-dependent effective temperature HOSS equations of motion for one-time variables Monte Carlo integrals in one- and two-time dynamics AGING URN MODELS The backgammon model Two-time dynamics and FDR effective temperature A model for collective modes Occupation probability density equations Ansatz for the adiabatic approximation Approach to equilibrium of occupation densities Probability distribution of proposed energy updates GLASSINESS IN A DIRECTED POLYMER MODEL The directed polymer model Directed polymer dynamics Cooling and heating setups POTENTIAL ENERGY LANDSCAPE APPROACH Potential energy landscape Thermodynamics in supercooled liquids The solid amorphous phase Fragility in the PEL PEL approach to the random orthogonal model PEL approach to the harmonic oscillator models Many-body glassy models THEORIES OF THE GLASSY STATE Mode coupling theory Replica theory for glasses with quenched disorder Glass models without quenched disorder: clone theory Frustration limited domain theory Random first order transition theory BIBLIOGRAPHY INDEX Author Biography: University of Rome 'La Sapienza', Italy University of Amsterdam, Netherlands