Extended Irreversible Thermodynamics

by Jou, David; Casas-Vazquez, Jose; Lebon, Georgy

• ISBN13: 9789048130733
• ISBN10: 9048130735
• Edition: 4th
• Format: Hardcover
• Copyright: 2010-02-03
• Publisher: Springer Nature

Summary

This is the 4th edition of the highly acclaimed monograph on Extended Irreversible Thermodynamics, a theory that goes beyond the classical theory of irreversible processes. In contrast to the classical approach, the basic variables describing the system are complemented by non-equilibrium quantities. The claims made for extended thermodynamics are confirmed by the kinetic theory of gases and statistical mechanics. The book covers a wide spectrum of applications, and also contains a thorough discussion of the foundations and the scope of the current theories on non-equilibrium thermodynamics.For this new edition, the authors critically revised existing material while taking into account the most recent developments in fast moving fields such as microfluidics, heat transport in micro- and nanosystems or fast solidification fronts in materials sciences. Several fundamental chapters have been revisited emphasizing physics and applications over mathematical derivations. Also, fundamental questions on the definition of non-equilibrium temperature, entropy, fluctuations of fluxes and boundary conditions are revisited and presented in a modern way.Detailed solutions for more than 130 problem sets presented in this book, as well as a wide bibliography on extended irreversible thermodynamics are accessible at the www.uab.es/dep-fisica/eit website.

Table of Contents

General Theory
Classical, Rational and Hamiltonian Formulations of Non-equilibrium Thermodynamics	p. 3
The General Balance Laws of Continuum Physics	p. 4
The One-Component System	p. 5
The Multicomponent Mixture	p. 8
Charged Systems	p. 10
The Law of Balance of Entropy	p. 13
Classical Irreversible Thermodynamics	p. 14
The Local-Equilibrium Hypothesis	p. 14
Entropy Production and Entropy Flux	p. 15
Linear Constitutive Equations	p. 17
Constraints on the Phenomenological Coefficients	p. 20
The Onsager-Casimir Reciprocal Relations	p. 20
Limitations	p. 22
Rational Thermodynamics	p. 23
The Basic Axioms of Rational Thermodynamics	p. 24
Constitutive Equations	p. 28
Critical Remarks	p. 30
A Hamiltonian Formulation: the GENERIC Formalism	p. 32
Problems	p. 35
Extended Irreversible Thermodynamics: Evolution Equations	p. 41
Heat Conduction in Rigid Solids	p. 42
Motivations	p. 42
The Generalised Gibbs Equation	p. 48
One-Component Viscous Fluid	p. 53
The Generalised Entropy Flux and Entropy Production	p. 55
Linearized Evolution Equations of the Fluxes	p. 57
Rational Extended Thermodynamics	p. 59
Heat Conduction	p. 59
Viscous Fluids	p. 63
Some Comments and Perspectives	p. 64
Problems	p. 67
Extended Irreversible Thermodynamics: Non-equilibrium Equations of State	p. 71
Physical Interpretation of the Non-equilibrium Entropy	p. 71
Non-equilibrium Equations of State: Temperature	p. 74
Zeroth Law, Second Law, and Temperature	p. 75
Evaluation of $ in Some Special Situations	p. 79
Alternative Definitions of Generalised Temperature	p. 79
Experimental Hints for the Non-equilibrium Temperature	p. 81
Non-equilibrium Equations of State: Thermodynamic Pressure	p. 82
Concavity Requirements and Stability	p. 85
Heat Conduction in a Rigid Solid	p. 86
Heat Conduction in Ideal Gases	p. 87
Shear Viscous Pressure in Viscous Fluids	p. 88
Problems	p. 89
Microscopic Foundations
The Kinetic Theory of Gases	p. 93
The Basic Concepts of Kinetic Theory	p. 93
Balance Equations	p. 95
The H-Theorem and the Second Law	p. 96
Non-equilibrium Entropy and the Entropy Flux	p. 98
Grad's Solution	p. 99
The Relaxation-Time Approximation	p. 104
Dilute Non-ideal Gases	p. 106
Entropy and Evolution Equations	p. 107
Microscopic Identification of Coefficients	p. 109
Non-linear Transport	p. 110
Beyond the Thirteen-Moment Approximation	p. 114
Problems	p. 119
Fluctuation Theory	p. 123
Einstein's Formula: Second Moments of Equilibrium Fluctuations	p. 123
Ideal Gases	p. 128
Fluctuations and Hydrodynamic Stochastic Noise	p. 131
The Entropy Flux	p. 131
Application to a Radiative Gas	p. 133
Onsager's Relations	p. 135
Experimental Observations of Fluctuations of the Fluxes and Flux Fluctuation Theorem	p. 137
Problems	p. 139
Information Theory	p. 143
Basic Concepts	p. 143
Ideal Gas Under Heat Flux and Viscous Pressure	p. 148
Ideal Gas Under Shear Flow: Non-linear Analysis	p. 150
Ideal Gas Submitted to a Heat Flux: Non-linear Analysis	p. 153
Relativistic Ideal Gas Under an Energy Flow	p. 154
Heat Flow in a Linear Harmonic Chain	p. 157
Information Theory and Non-equilibrium Fluctuations	p. 162
Problems	p. 166
Linear Response Theory	p. 169
Projection Operator Methods	p. 169
Evolution Equations for Simple Fluids	p. 175
Continued-Fraction Expansions	p. 179
Problems	p. 181
Computer Simulations	p. 183
Computer Simulations of Non-equilibrium Steady States	p. 183
Non-equilibrium Equations of State	p. 185
Dependence of the Free Energy on the Shear Rate: Non-linear Approach	p. 188
Shear-Induced Heat Flux and the Zeroth Law	p. 190
Problems	p. 192
Selected Applications
Hyperbolic Heat Transport in Rigid Conductors	p. 199
Linear Wave Propagation: Second Sound and Telegrapher Equation	p. 200
Transient Heat Conduction: Parabolic Versus Hyperbolic Regimes	p. 202
Formulation of the Problem in Absence of Internal Source	p. 202
Results for Diamond Films	p. 204
Heating in Presence of Internal Energy Source: Application to Thermal Ignition	p. 205
Beyond the Cattaneo Equation	p. 208
Guyer-Krumhansl's Model	p. 209
A Generalised Guyer-Krumhansl's Model	p. 210
Other Examples of Flux Limiters	p. 219
Phonon Hydrodynamics	p. 222
Two-Temperature Models	p. 223
Other Applications	p. 224
Problems	p. 225
Heat Transport in Micro- and Nano-systems	p. 233
EIT Description of Heat Conduction at Micro- and Nano-scales	p. 234
Effective Heat Conductivity	p. 235
Transient Temperature Distribution in a Micro Film	p. 239
The Equation of Phonon Radiative Transfer	p. 241
The Ballistic Diffusion Equation	p. 245
The Model Equations	p. 246
Illustration: Transient Heat Transport in Thin Films	p. 249
Problems	p. 251
Waves in Fluids: Sound, Ultrasound, and Shock Waves	p. 253
Sound Propagation in Fluids: Linear Waves	p. 253
The Classical Theory	p. 254
Extended Thermodynamic Theory	p. 256
Particular Results for Monatomic Gases	p. 258
Non-linear Acceleration Waves in Monatomic Ideal Gases	p. 262
ShockWaves	p. 264
The Classical Navier-Fourier-Stokes Approach	p. 264
The Extended Irreversible Thermodynamics Approach	p. 266
Shock Structure	p. 269
Problems	p. 271
Generalised Hydrodynamics	p. 275
Density and Current Correlation Functions	p. 275
Spectral Density Correlation	p. 277
The Classical Hydrodynamical Approximation	p. 277
The EIT Description	p. 280
The Transverse Velocity Correlation Function: The EIT Description	p. 282
The Longitudinal Velocity Correlation Function: The EIT Description	p. 285
Influence of Higher-Order Fluxes	p. 288
Problems	p. 289
Non-classical Diffusion, Thermo-diffusion and Suspensions	p. 291
Molecular Diffusion in Perfect Fluid Mixtures	p. 292
Telegrapher's Equation and Stochastic Processes	p. 297
Correlated Random Walk	p. 298
H-Theorem for Telegrapher Type Equation	p. 299
Non-Fickian Diffusion in Polymers	p. 301
Hyperbolic Reaction-Diffusion Systems	p. 306
Thermo-diffusion in Binary Mixtures	p. 308
Suspensions of Solid Particles in Fluids	p. 311
Suspensions Versus Molecular Diffusion	p. 312
EIT Description of Suspensions	p. 313
Comparison with Other Models	p. 316
Microstructure in Rapid Solidification of Binary Alloys	p. 318
Problems	p. 321
Electrical Systems and Micro-devices Modelization	p. 327
Electrical Systems: Evolution Equations	p. 327
Cross Terms in Constitutive Equations: Onsager's Relations	p. 331
Hydrodynamical Models of Transport in Semiconductors and Plasmas	p. 334
Transport in Semiconductors	p. 334
Transport in Plasmas	p. 338
Dielectric Relaxation of Polar Liquids	p. 340
Problems	p. 343
From Thermoelastic Solids to Rheological Materials	p. 347
Thermoelasticity	p. 348
Viscoelasticity	p. 351
Plasticity	p. 354
Relation of EIT to Kinetic Polymer Models	p. 359
The Rouse and Zimm Models	p. 359
EIT Description of the Rouse and Zimm Models	p. 360
Kinetic Justification of the EIT Results	p. 361
Non-Newtonian Fluids	p. 365
General Considerations	p. 365
EIT Description of Second-Order Non-Newtonian Fluids	p. 369
Problems	p. 376
Thermodynamics of Polymer Solutions Under Shear Flow	p. 383
The Chemical Potential Under Shear	p. 384
Explicit Solution for the Rouse-Zimm Model	p. 388
Chemical Reactions Under Flow	p. 393
Shear-Induced Effect on the Affinity	p. 393
Illustration: Polymer Degradation Under Flow	p. 394
Dynamical Approach	p. 397
Shear-Induced Migration of Polymers	p. 399
Problems	p. 403
Relativistic Formulation	p. 407
The Macroscopic Theory	p. 408
Characteristic Speeds	p. 411
Relativistic Kinetic Theory	p. 414
Nuclear Matter and Relativistic Ion Collisions	p. 417
Problems	p. 419
Viscous Cosmological Models and Cosmological Horizons	p. 423
Viscous Cosmological Models and Accelerated Expansion	p. 424
Particle Production and Effective Bulk Viscosity	p. 430
Extended Thermodynamics and Cosmological Horizons	p. 432
Astrophysical Problems: Gravitational Collapse	p. 435
Problems	p. 436
Summary of Vector and Tensor Notation	p. 439
Symmetric and Antisymmetric Tensors	p. 439
Decomposition of a Tensor	p. 439
Scalar (or Dot) and Tensorial (Inner) Products	p. 440
(Inner) Tensorial Product (also Named Dyadic Product)	p. 441
Cross Multiplication Between Two Vectors and Between a Tensor and a Vector	p. 441
Differentiation	p. 441
Tensor Invariants	p. 442
Useful Integrals in the Kinetic Theory of Gases	p. 443
Some Physical Constants	p. 445
References	p. 447
Author Index	p. 469
Subject Index	p. 477
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