Extended Irreversible Thermodynamics

ISBN-13: 9783642625053 / Angielski / Miękka / 2012 / 463 str.

D. Jou; J. Casas-Vazquez; G. Lebon

Opis

Covers a wide spectrum of applications and contains a wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The new edition reflects new developments and contains a new chapter on the interplay between hydrodynamics and thermodynamics.

Recenzje

From the reviews of the second edition
"This excellent book presents the actual state of ideas on thermo-dynamics, and the new concept of Extended Irreversible Thermo-dynamics (EIT) ... Each chapter is self-consistent and ends with specific exercises and references."
(V. Pletser in: Physicalia)

From the reviews of the third edition:

"This is an excellent monograph presenting comprehensively the state-of-art in one of the fast developing branches of non-equilibrium thermodynamics. The name of the theory emphasizes the main idea exploiting in the description on non-equilibrium states, namely, the extension of classical thermodynamic state space by means of additional independent variables, such as heat flux, entropy flux, and so on. ... Three parts of the book include the general theory, microscopic foundation, and selected applications. ... recommended for using in advanced courses for graduate students." (Arkadi Berezovski, Zentralblatt MATH, Vol. 974, 2001)

Spis treści

I. General Theory.- 1 Classical and Rational Formulations of Non-equilibrium Thermodynamics.- 1.1 The General Balance Laws of Continuum Physics.- 1.2 The Law of Balance of Entropy.- 1.3 Classical Irreversible Thermodynamics.- 1.4 Rational Thermodynamics.- Problems.- 2 Extended Irreversible Thermodynamics: Evolution Equations.- 2.1 Heat Conduction.- 2.2 One-component Viscous Fluid.- 2.3 The Generalised Entropy Flux and Entropy Production.- 2.4 Linearized Evolution Equations of the Fluxes.- 2.5 Rational Extended Thermodynamics.- 2.6 Some Comments and Perspectives.- 2.7 Entropy Evolution in an Isolated System: An Illustrative Example.- Problems.- 3 Extended Irreversible Thermodynamics: Non-equilibrium Equations of State.- 3.1 Physical Interpretation of the Non-equilibrium Entropy.- 3.2 Non-equilibrium Equations of State: Temperature.- 3.3 Non-equilibrium Equations of State: Thermodynamic Pressure.- 3.4 Convexity Requirements and Stability.- Problems.- 4 Hamiltonian Formulations.- 4.1 GENERIC Formulation.- 4.2 Reversible and Irreversible Kinematics.- 4.3 Governing Equations of EIT.- Problems.- II. Microscopic Foundations.- 5 The Kinetic Theory of Gases.- 5.1 The Basic Concepts of Kinetic Theory.- 5.2 Non-equilibrium Entropy and the Entropy Flux.- 5.3 Grad’ Solution.- 5.4 The Relaxation-Time Approximation.- 5.5 Dilute Non-ideal Gases.- 5.6 Non-linear Transport.- 5.7 Beyond the Thirteen-Moment Approximation: Continued-Fraction Expansions of Transport Coefficients.- Problems.- 6 Fluctuation Theory.- 6.1 Einstein’ Formula. Second Moments of Equilibrium Fluctuations.- 6.2 Ideal Gases.- 6.3 Fluctuations and Hydrodynamic Stochastic Noise.- 6.4 The Entropy Flux.- 6.5 Application to a Radiative Gas.- 6.6 Onsager’ Relations.- Problems.- 7 Information Theory.- 7.1 Basic Concepts.- 7.2 Ideal Gas Under Heat Flux and Viscous Pressure.- 7.3 Ideal Gas Under Shear Flow: Non-linear Analysis.- 7.4 Ideal Gas Submitted to a Heat Flux: Non-linear Analysis.- 7.5 Relativistic Ideal Gas Under an Energy Flow.- 7.6 Heat Flow in a Linear Harmonic Chain.- 7.7 Information Theory and Non-equilibrium Fluctuations.- Problems.- 8 Linear Response Theory.- 8.1 Projection Operator Methods.- 8.2 Evolution Equations for Simple Fluids.- 8.3 Continued-Fraction Expansions.- Problems.- 9 Computer Simulations.- 9.1 Computer Simulations of Non-equilibrium Steady States.- 9.2 Non-equilibrium Equations of State.- 9.3 Dependence of the Free Energy on the Shear Rate: Non-linear Approach.- 9.4 Shear-Induced Heat Flux and the Zeroth Law.- Problems.- III. Selected Applications.- 10 Hyperbolic Heat Conduction.- 10.1 The Finite Speed of Thermal Signals. Second Sound.- 10.2 Heat Pulses.- 10.3 Beyond the Maxwell-Cattaneo Equation.- 10.4 Second Sound Under a Heat Flow.- 10.5 Heat Conduction in a Rotating Rigid Cylinder.- 10.6 Non-linear Heat Transfer: Flux Limiters.- 10.7 Other Applications.- Problems.- 11 Waves in Fluids.- 11.1 Hydrodynamic Modes in Simple Fluids.- 11.2 Transverse Viscoelastic Waves.- 11.3 Ultrasound Propagation in Monatomic Gases.- 11.4 Shock Waves.- Problems.- 12 Generalised Hydrodynamics.- 12.1 Density and Current Correlation Functions.- 12.2 Spectral Density Correlation.- 12.3 The Transverse Velocity Correlation Function: the EIT Description.- 12.4 The Longitudinal Velocity Correlation Function: the EIT Description.- 12.5 Influence of Higher-order Fluxes.- Problems.- 13 Non-classical Diffusion.- 13.1 Extended Thermodynamics of Diffusion.- 13.2 Telegrapher’ Equation and Stochastic Processes.- 13.3 Taylor’ Dispersion.- 13.4 Non-Fickian Diffusion in Polymers.- 13.5 Hyperbolic Reaction-Diffusion Systems.- Problems.- 14 Electrical Systems.- 14.1 Electrical Systems: Evolution Equations.- 14.2 Cross Terms in Constitutive Equations: Onsager’ Relations.- 14.3 Hydrodynamical Models of Transport in Semiconductors and Plasmas.- 14.4 Dielectric Relaxation of Polar Liquids.- Problems.- 15 Rheological Materials.- 15.1 Rheological Models.- 15.2 EIT Description of Linear Viscoelasticity.- 15.3 The Rouse-Zimm Relaxational Model.- 15.4 EIT Description of Second-Order Non-Newtonian Fluids.- Problems.- 16 Thermodynamics of Polymer Solutions Under Shear Flow.- 16.1 The Chemical Potential Under Shear: Flow-Induced Changes in the Phase Diagram of Solutions.- 16.2 Explicit Solution for the Rouse-Zimm Model.- 16.3 Chemical Reactions Under Flow.- 16.4 Dynamical Approach.- 16.4 Shear-Induced Migration of Polymers.- Problems.- 17 Relativistic Formulation.- 17.1 The Macroscopic Theory.- 17.2 Characteristic Speeds.- 17.3 Relativistic Kinetic Theory.- 17.4 Nuclear Matter.- Problems.- 18 Viscous Cosmological Models.- 18.1 Cosmological Applications: Viscous Models.- 18.2 Particle production and Effective Bulk Viscosity.- 18.3 Extended Thermodynamics and Cosmological Horizons.- 18.4 Astrophysical Problems: Gravitational Collapse.- Problems.- References.- Appendices.- A. Summary of Vector and Tensor Notation.- B. Useful Integrals in the Kinetic Theory of Gases.- C. Some Physical Constants.

O autorze

The new edition reflects new developments in theory and applications, it adds new problems and contains a new chapter on the interplay between hydrodynamics and thermodynamics, a field of active research.

Blurb

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. The basic variables describing the system are no longer the equilibrium conserved variables: the latter are complemented by non-equilibrium quantities, such as the heat flux, the viscous pressure tensor, the matter flux, the electric current flux, etc. 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 such as hyperbolic heat conduction, rheological models, waves in fluids, generalized hydrodynamics, phase diagrams of solutions under shear, non-Fickian diffusion, electrical systems, and a relativistic formulation including some cosmological applications. The book also contains a wide discussion of the foundations and the scope of the current theories on non-equilibrium thermodynamics (classical irreversible thermodynamics and rational thermodynamics).
The present edition reflects new developments in the theory and applications, adds new problems and provides a more detailed comparison with other fields of active research. It contains one hundred thirty proposed problems, whose detailed solutions, as well as wide bibliography on extended irreversible thermodynamics and related topics,may be unloaded from the www.uab.es/dep-fisica/eit website.