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.

Preface	p. V
Acknowledgements	p. VII
Acronyms	p. XI
Symbols	p. XIII
Introduction	p. 1
Theory and phenomenology of glasses	p. 15
Processes, timescales and transitions	p. 15
Dynamical glass transition	p. 17
Thermal glass transition	p. 19
Strong and fragile glass formers	p. 23
Aging	p. 26
Time sector separation	p. 28
Configurational entropy	p. 29
Kauzmann paradox	p. 30
Static phase transition and Kauzmann temperature	p. 31
"Classic" versus "modern" configurational entropy	p. 31
An intrinsically dynamic "state" function	p. 33
Adam-Gibbs entropic theory	p. 34
Absence of flow in cathedral glasses	p. 37
Fragility index	p. 38
Kovacs effect	p. 39
Two temperature thermodynamics	p. 43
Elements of thermodynamics	p. 46
First law and second law	p. 46
Clausius-Clapeyron relation	p. 47
Maxwell relation	p. 48
Keesom-Ehrenfest relations and Prigogine-Defay ratio	p. 48
Fictive temperature	p. 50
Two temperature thermodynamics	p. 53
Two temperature thermodynamics for glassy systems	p. 55
Laws of thermodynamics for off-equilibrium systems	p. 56
Maxwell relation for aging systems	p. 58
Generalized Clausius-Clapeyron relation	p. 59
Keesom-Ehrenfest relations and Prigogine-Defay ratio out of equilibrium	p. 60
Laws of thermodynamics for glassy magnets	p. 64
Effective temperature in thermal cycles	p. 65
Fluctuation formula and effective temperatures	p. 70
Fluctuation and dissipation out of equilibrium	p. 72
Fluctuation-dissipation ratio	p. 74
Limits to the role of FDR as a temperature	p. 81
Direct measurement of the effective temperature	p. 83
Asymptotic solution in nonlinear cooling	p. 87
Exactly solvable models for the glassy state	p. 89
Harmonic oscillator model	p. 91
Analytically solvable Monte Carlo dynamics	p. 92
Parallel Monte Carlo versus Langevin dynamics	p. 96
Kinetic models with separation of timescales	p. 99
Statics and phase space constraint	p. 101
Parallel Monte Carlo dynamics of the HOSS model: equations of motion	p. 104
Dynamics of the strong glass model	p. 106
Dynamics of the fragile glass model	p. 109
Adam-Gibbs relation in the HOSS model	p. 115
Out-of-equilibrium thermodynamics	p. 116
Quasi-static approach	p. 116
Effective temperature from generalized laws	p. 118
Dynamic transition rate and effective temperature	p. 120
FDR and effective temperature	p. 123
Heat flow of [alpha] processes	p. 131
Effective temperature from a fluctuation formula	p. 131
Below the Kauzmann transition	p. 132
Instantaneous relaxation time	p. 134
Kovacs effect: limits of two temperature thermodynamics	p. 135
Analytical solution in the long-time regime	p. 138
Effective temperature and effective field	p. 140
Measuring effective temperature in HO models	p. 142
Heat flux between off-equilibrium systems	p. 144
Mode-dependent effective temperature	p. 146
Quasi-static effective temperature	p. 148
Mode-dependent fluctuation-dissipation ratio	p. 149
Transition rate effective temperature	p. 150
HOSS equations of motion for one-time variables	p. 152
Strong glass	p. 152
Fragile glass	p. 152
Analytic expressions for the Kovacs effect	p. 157
Monte Carlo integrals in one- and two-time dynamics	p. 158
Coefficients of the two-time variables equations	p. 160
Aging urn models	p. 163
The backgammon model	p. 166
Equilibrium thermodynamics	p. 167
Dynamics	p. 170
Adiabatic approximation and effective temperature	p. 174
Entropic barriers and a microcanonic derivation of the equation of motion	p. 178
Backgammon random walker	p. 179
Two-time dynamics and FDR effective temperature	p. 181
Effective temperature(s) in the backgammon model	p. 184
A model for collective modes	p. 185
Observables and equilibrium	p. 187
Dynamics of the disordered backgammon model	p. 190
Relaxational spectrum in equilibrium	p. 196
Specific examples of continuous energy distribution	p. 197
A method to determine the threshold energy scale	p. 201
Occupation probability density equations	p. 203
Ansatz for the adiabatic approximation	p. 205
Approach to equilibrium of occupation densities	p. 207
Probability distribution of proposed energy updates	p. 208
Glassiness in a directed polymer model	p. 211
The directed polymer model	p. 212
Disordered situation and Lifshitz-Griffiths singularities	p. 213
Static phase diagram	p. 216
Dual view in temperature	p. 218
Directed polymer dynamics	p. 219
Cooling and heating setups	p. 223
Poincare recurrence time	p. 223
Potential energy landscape approach	p. 225
Potential energy landscape	p. 228
Steepest descent	p. 229
Features of the PEL description borrowed from vitreous properties	p. 231
Inter- and intra-basins transitions: scales separation	p. 232
Inherent structures distribution: formal treatment	p. 233
Harmonic approximation	p. 236
Thermodynamics in supercooled liquids	p. 237
Inherent structure pressure	p. 237
Random energy model and Gaussian approximation	p. 239
Equation of state	p. 241
IS equation of State	p. 243
The solid amorphous phase	p. 244
PEL effective temperature from direct comparison to the aging dynamics	p. 245
PEL effective temperature and pressure in the two temperature thermodynamic framework	p. 246
The pressure in glasses	p. 249
Fragility in the PEL	p. 251
PEL approach to the random orthogonal model	p. 253
Effective temperature in the ROM	p. 254
PEL approach to the harmonic oscillator models	p. 256
PEL effective temperature in the HOSS model	p. 259
Quasi-static definition of IS effective temperature	p. 261
Many-body glassy models	p. 264
Soft spheres	p. 265
Lennard-Jones many-body interaction potential	p. 266
Lewis-Wahnstrom model for orthoterphenyl	p. 267
Simple point charge extended model for water	p. 268
Theories of the glassy state	p. 269
Mode-coupling theory	p. 269
Replica theory for glasses with quenched disorder	p. 274
The random energy model	p. 275
The p-spin model	p. 276
Complexity	p. 279
Mean-field scenario	p. 281
Glass models without quenched disorder: clone theory	p. 283
Equilibrium thermodynamics of the cloned m-liquid	p. 283
Analytic tools and specific behaviors in cloned glasses	p. 285
Effective temperature for the cloned molecular liquid	p. 287
Frustration limited domain theory	p. 289
Geometric frustration	p. 289
Avoided critical point	p. 291
Critical assessment of the approach	p. 294
Heuristic scaling arguments	p. 297
Random first order transition theory	p. 298
Adam-Gibbs theory, revisited	p. 300
Entropic driven "nucleation" and mosaic state	p. 301
Density functional for the RFOT theory	p. 305
Beyond entropic driving I: droplet partition function	p. 311
Beyond entropic driving II: library of local states	p. 315
Bibliography	p. 319
Index	p. 339
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Thermodynamics of the Glassy State

9780750309974

0750309970

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