Extended Irreversible Thermodynamics

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

• ISBN13: 9783540411567
• ISBN10: 3540411569
• Edition: 3rd
• Format: Hardcover
• Copyright: 2001-07-01
• Publisher: Springer Verlag

Summary

This is the first comprehensive monograph on a new thermodynamic theory that goes beyond the classical theory of irreversible processes. In contrast to the classical approach, the local equilibrium hypothesis is abandoned, and the basic variables 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 wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The present edition reflects new developments in the theory of applications, adds new problems and provides a more detailed comparison with other fields of active research. It contains 130 proposed problems, whose detailed solutions, as well as wide bibliography on extended irreversible thermodynamics and related topices, may be unloaded from the www.uab.es/dep-fisica/eit website.

Table of Contents

Part I. General Theory
Classical and Rational Formulations of Non-equilibrium Thermodynamics	3	(36)
The General Balance Laws of Continuum Physics	4	(9)
The Law of Balance of Entropy	13	(2)
Classical Irreversible Thermodynamics	15	(9)
Rational Thermodynamics	24	(15)
Problems	33	(6)
Extended Irreversible Thermodynamics: Evolution Equations	39	(34)
Heat Conduction	40	(7)
One-component Viscous Fluid	47	(2)
The Generalised Entropy Flux and Entropy Production	49	(3)
Linearized Evolution Equations of the Fluxes	52	(2)
Rational Extended Thermodynamics	54	(11)
Some Comments and Perspectives	65	(1)
Entropy Evolution in an Isolated System: An Illustrative Example	66	(7)
Problems	70	(3)
Extended Irreversible Thermodynamics: Non-equilibrium Equations of State	73	(20)
Physical Interpretation of the Non-equilibrium Entropy	74	(3)
Non-equilibrium Equations of State: Temperature	77	(6)
Non-equilibrium Equations of State: Thermodynamic Pressure	83	(4)
Convexity Requirements and Stability	87	(6)
Problems	92	(1)
Hamiltonian Formulations	93	(20)
GENERIC Formulation	94	(4)
Reversible and Irreversible Kinematics	98	(9)
Governing Equations of EIT	107	(6)
Problems	109	(4)
Part II. Microscopic Foundations
The Kinetic Theory of Gases	113	(32)
The Basic Concepts of Kinetic Theory	114	(4)
Non-equilibrium Entropy and the Entropy Flux	118	(2)
Grad's Solution	120	(5)
The Relaxation-Time Approximation	125	(2)
Dilute Non-ideal Gases	127	(5)
Non-linear Transport	132	(5)
Beyond the Thirteen-Moment Approximation: Continued-Fraction Expansions of Transport Coefficients	137	(8)
Problems	142	(3)
Fluctuation Theory	145	(20)
Einstein's Formula. Second Moments of Equilibrium Fluctuations	146	(4)
Ideal Gases	150	(4)
Fluctuations and Hydrodynamic Stochastic Noise	154	(1)
The Entropy Flux	155	(2)
Application to a Radiative Gas	157	(1)
Onsager's Relations	158	(7)
Problems	161	(4)
Information Theory	165	(26)
Basic Concepts	166	(4)
Ideal Gas Under Heat Flux and Viscous Pressure	170	(2)
Ideal Gas Under Shear Flow: Non-linear Analysis	172	(3)
Ideal Gas Submitted to a Heat Flux: Non-linear Analysis	175	(1)
Relativistic Ideal Gas Under an Energy Flow	176	(3)
Heat Flow in a Linear Harmonic Chain	179	(7)
Information Theory and Non-equilibrium Fluctuations	186	(5)
Problems	190	(1)
Linear Response Theory	191	(16)
Projection Operator Methods	192	(5)
Evolution Equations for Simple Fluids	197	(5)
Continued-Fraction Expansions	202	(5)
Problems	204	(3)
Computer Simulations	207	(18)
Computer Simulations of Non-equilibrium Steady States	208	(1)
Non-equilibrium Equations of State	209	(4)
Dependence of the Free Energy on the Shear Rate: Non-linear Approach	213	(2)
Shear-Induced Heat Flux and the Zeroth Law	215	(10)
Problems	218	(7)
Part III. Selected Applications
Hyperbolic Heat Conduction	225	(28)
The Finite Speed of Thermal Signals. Second Sound	226	(3)
Heat Pulses	229	(5)
Beyond the Maxwell---Cattaneo Equation	234	(6)
Second Sound Under a Heat Flow	240	(2)
Heat Conduction in a Rotating Rigid Cylinder	242	(2)
Non-linear Heat Transfer: Flux Limiters	244	(2)
Other Applications	246	(7)
Problems	248	(5)
Waves in Fluids	253	(24)
Hydrodynamic Modes in Simple Fluids	253	(2)
Transverse Viscoelastic Waves	255	(2)
Ultrasound Propagation in Monatomic Gases	257	(9)
Shock Waves	266	(11)
Problems	274	(3)
Generalised Hydrodynamics	277	(18)
Density and Current Correlation Functions	278	(2)
Spectral Density Correlation	280	(5)
The Transverse Velocity Correlation Function: the EIT Description	285	(3)
The Longitudinal Velocity Correlation Function: the EIT Description	288	(3)
Influence of Higher-order Fluxes	291	(4)
Problems	293	(2)
Non-classical Diffusion	295	(22)
Extended Thermodynamics of Diffusion	296	(2)
Telegrapher's Equation and Stochastic Processes	298	(5)
Taylor's Dispersion	303	(3)
Non-Fickian Diffusion in Polymers	306	(5)
Hyperbolic Reaction---Diffusion Systems	311	(6)
Problems	314	(3)
Electrical Systems	317	(22)
Electrical Systems: Evolution Equations	318	(4)
Cross Terms in Constitutive Equations: Onsager's Relations	322	(3)
Hydrodynamical Models of Transport in Semiconductors and Plasmas	325	(6)
Dielectric Relaxation of Polar Liquids	331	(8)
Problems	335	(4)
Rheological Materials	339	(34)
Rheological Models	340	(5)
EIT Description of Linear Viscoelasticity	345	(8)
The Rouse---Zimm Relaxational Model	353	(7)
EIT Description of Second-Order Non-Newtonian Fluids	360	(13)
Problems	369	(4)
Thermodynamics of Polymer Solutions Under Shear Flow	373	(26)
The Chemical Potential Under Shear: Flow-Induced Changes in the Phase Diagram of Solutions	374	(5)
Explicit Solution for the Rouse---Zimm Model	379	(5)
Chemical Reactions Under Flow	384	(4)
Dynamical Approach	388	(2)
Shear-Induced Migration of Polymers	390	(9)
Problems	395	(4)
Relativistic Formulation	399	(16)
The Macroscopic Theory	400	(3)
Characteristic Speeds	403	(4)
Relativistic Kinetic Theory	407	(4)
Nuclear Matter	411	(4)
Problems	413	(2)
Viscous Cosmological Models	415	(16)
Cosmological Applications: Viscous Models	416	(7)
Particle production and Effective Bulk Viscosity	423	(2)
Extended Thermodynamics and Cosmological Horizons	425	(3)
Astrophysical Problems: Gravitational Collapse	428	(3)
Problems	428	(3)
References	431	(20)
Appendices	451	(6)
A. Summary of Vector and Tensor Notation	451	(4)
B. Useful Integrals in the Kinetic Theory of Gases	455	(1)
C. Some Physical Constants	456	(1)
Subject Index	457