Table Of ContentExtendedIrreversibleThermodynamics
ONLINE L1BRARY
Physics and Astronomy
http://www.springer.de/phys/
Springer-Verlag Berlin Heidelberg GmbH
D. lou J. Casas-Vazquez G. Lebon
Extended Irreversible
Thermodynamics
Third, Revised andEnlargedEdition
With 30 Figuresand15Tables
i
Springer
Professor Dr. David Iou
Professor Dr. Iose Casas-Vazquez
Departament de Fisica
Grup de Fisica Estadistica
Universitat Autonoma de Barcelona
Edifiei C
08193 Bellaterra, Catalonia, Spain
Professor Dr. Georgy Lebon
Departement de Physique
Universite de Lii~ge
Sart Tilman B5
4000 Liege, Belgium
Library of Congress Cataloging-in-Publication Data. Jou, D. (David). Extended irreversible thermody
namicsl D. Iou, I. Casas-Vazquez, G. Lebon. - 3rd ed. p. cm. Includes bibliographical references and
index. ISBN 978-3-642-62505-3 1. Irreversible processes. I. Casas-Vazquez, J. Oose), 1938-II. Lebon,
G. (Georgy) III. Title. QC318.I7 J67 2000 536'.7-dc21 00-053784
ISBN 978-3-642-62505-3 ISBN 978-3-642-56565-6 (eBook)
DOI 10.1007/978-3-642-56565-6
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Originally published by Springer-Ve rlag Berlin Heidelberg New York in 2001
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Prefaceto the ThirdEdition
In writing this third edition, weproceeded having in mind two main objectives: peda
gogyandphysics.Oneofouressentialconcernsisindeedtoopen thesubject toalarge
audience of scientists with adiversity ofinterests.This is thereason we have empha
sizedthepedagogical aspects,startingwiththesimplestsituationsbefore treating more
complex problems. Our aim is to show that thermodynamics is not restricted to the
study of purely thermal phenomena but that it largely covers many different areas,
going from continuum mechanics to statistical physics, from nuclear collisions to
cosmology, bypassing,forinstance,throughchemistry,rheologyandbiology.
Our second objective is tostressthephysicalaspects in their broadest sense,i.e,
trying to clarify the foundations and relating the theoretical results with experimental
data and applications, rather than introducing formal and lengthy developments. Im
portant sections ofthebookaredevoted tothediscussionoffundamental notions,such
asthe selection ofbasicvariables, thedefinitionofentropy, temperature, pressure, and
chemical potential outside equilibrium and the statement of the second law. We feel
that these crucial questions deserve special attention when they cross the borders of
classical theories. We haveincluded new original results and opened the door to new
extensions andapplications.
For the student ortheresearcherit maybestimulatingtogobeyond theclassical
theories and todiscover adomain of newideas, new applications, and newproblems.
This is what extended irreversible thermodynamics (EIT)offers nowadays:it does not
pretendtosolvealltheproblemsraisedincontinuumphysicsandstatistical mechanics,
but it can be viewed as an emergent new global framework of non-equilibrium
thermodynamics and arapidly advancing frontier with new applications being treated
andfundamental questionsbeingaskedandtentativelyclarified.
This edition hasbeenextensivelyremodelledcompared tothefirst two. Wehave
gone from 12to 18chapters as a result of splitting some of the former chapters into
shorter ones andfocusing betteronthefoundationsandontheintroduction tothebasic
ideas of the latest developments. Asfor the two preceding editions, we have clearly
separatedthe structure ofthe bookintothreeparts, namely thegeneral theory (PartI),
microscopic foundations (Part II), and selected applications (Part III). Amongst the
VI PrefacetotheThirdEdition
most visible changes, wehave split thegeneral presentation ofEIT into two chapters:
Chap. 2 devoted to establishing the transport equations and dynamical aspects, and
Chap.3in which weintroduce thenon-equilibriumequations ofstateemphasizingthe
meaning of entropy and temperature in non-equilibrium states. Comparison with the
rational version of extended thermodynamics has beenmademore explicit. Chapter 4
showsanoverview ofHamiltonianformulations,whichhavedeveloped inrecent years
intoapromisingdomain.
The microscopic foundations arediscussedinChaps.5-9,withtwonewchapters
concerning information theory and computer simulations. Both topics were already
present intheformereditionsassubsectionsofotherchapters,butrecentdevelopments
havejustifiedarenewedandupdatedpresentation.
Applications cover half ofthebook:ninechapters from the totaleigthteen.They
show that the exploration of new theoretical grounds is both an intellectual challenge
and a source of new practical possibilities. Since contemporary technology strives
towards higher speed, power, and miniaturization, the transport equations must
incorporate memory, non-local, and non-linear effects. Compared to the generalised
transportequations incorporating theaforementionedeffects,EITplaysarole similarto
that played by classical irreversible thermodynamics with respect to the classical
transport equa-tions.Diffusion andelectrical phenomena,treated inasingle chapter in
theprevious editions,arethesubjectoftwodifferent, updatedchapters;therelativistic
formulation has also been split into two different chapters, one devoted to the
foundations and the other to cosmological applications. Finally, let us mention that a
wideoverview oftheliteratureonEITaswellasthesolutionstotheproposedproblems
canbefoundonthewww.uab.es/dep-fisica/eitwebsite.
This book, in its successive editions, has widely benefited from the fruitful sug
gestions and comments by colleagues, including M. Anile, J. Camacho, M. Criado
Sancho, L.S.Garcfa-Colfn,M.Grmela, P.T.Landsberg,R.Luzzi,W.Muschik, D. Pa
v6n, M.Torrisi, A.Valenti and manyothers.Weacknowledgethefinancial support of
theDGICyT oftheSpanishMinistryofEducationandCultureunderGrantNos.PB90
0676 and PB94-07l8, of the DGR of the Generalitat of Catalonia, under Grant Nos.
1997SGR 00378 and 2000SGR 00095, of the Belgian Ministry of Scientific Policy
under PAl Grant Nos. 21, 29 and IV 6, and a grant from the European Union in the
framework of theProgram ofHumanCapitalandMobility(EuropeanThermodynamic
NetworkERB-CHRXCT920(07).
Bellaterra,Barcelona
Liege DavidJou
March2001 Jose Casas-Ydzquez
GeorgyLebon
Preface to the FirstEdition
Classical irreversible thermodynamics, asdeveloped by Onsager, Prigogine and many
other authors,isbasedonthelocal-equilibriumhypothesis.Outofequilibrium, anysys
temisassumed todepend locallyonthesamesetofvariablesaswhenitisinequilibri
um. This leads to a formal thermodynamic structure identical to that of equilibrium:
intensive parameters such as temperature, pressure and chemical potentials are well
defined quantities keeping their usual meaning,thermodynamic potentials are derived
as Legendre transformations and all equilibrium thermodynamic relations retain their
validity.The theory based on thishypothesis has turned out to bevery useful and has
collected anumberofsuccessesinmanypracticalsituations.
However, therecentdecadehaswitnessedasurgeofinterestingoingbeyond the
classical formulation.There are several reasons for this.One of them is the develop
ment of experimental methods able to deal with the response of systems to high
frequency andshort-wavelengthperturbations,suchasultrasoundpropagation andlight
and neutron scattering.The observedresultshaveledtogeneralisations oftheclassical
hydrodynamical theories,byincludingmemoryfunctionsorgeneralised transportcoef
ficients depending on the frequency and the wavevector. This field has generated
impressive progress innon-equilibriumstatisticalmechanics,butfor themoment ithas
not brought about a parallel development in non-equilibrium thermodynamics. An
extension of thermodynamics compatible with generalised hydrodynamics therefore
appears tobeanaturalsubjectofresearch.
Anadditionalreason hasfosteredaninterestingeneralisingtheclassical transport
equations, like Fourier's law for heat conduction, Fick's law for diffusion, and
Newton'slawforviscousflow.Itiswellknownthatafterintroducing theserelations in
thebalanceequations, oneisledtoparabolicpartial-differentialequations which imply
that perturbations propagate with infinite speed.This behaviour is incompatible with
experimental evidenceanditisalsodisturbingfromatheoreticalpointofview,because
collectivemolecular effectsshould beexpectedtopropagateatfinitevelocity, not only
in a relativistic framework, but even from a non-relativistic point of view. This un
pleasant property can beavoided bytakingintoaccount thefinite nonvanishing relax-
VIII PrefacetotheFirstEdition
ationtimeoftherespectivefluxes,e.g,heatflux,diffusionflux,momentumflux,some
times generically called dissipative fluxes. The subsequentequations are however not
compatible withtheclassical non-equilibriumthennodynamics, sincetheyleadinsome
circumstancestonegativeentropy production.Thus,athermodynamic theory compati
blewiththese phenomena ishighlydesirable,becauseitmayprovidenewinsights into
the meaning and definition of fundamental thermodynamic quantities, as entropy and
temperature, and may clarify the limitsof validityofthe local-equilibrium hypothesis
andoftheusualformulationsofthesecondlawoutofequilibrium.
The former problems are not merely academic. It has been observed in several
systems that thedissipative fluxes arecharacterized bylong relaxation times.Typical
examples are polymeric fluids, heatandelectricconductorsatlowtemperature, super
conductors, andsoon.Anaccurateunderstandingofthesesystemsmaythusbeimport
ant not only from a theoretical point of view, but also for practical purposes. In real
situations,thesesystemsareoutofequilibrium.Accordingly,thereisanurgentneedfor
anon-equilibrium thermodynamictheoryable,ontheonehand,tocopewiththeeffects
oflongrelaxation timesand,ontheother,tocomplementotherformalismsbasedonthe
useofinternalvariables.
There areother reasons for thepresentstudy.Oneshould beaware thatclassical
irreversible thermodynamics is not the only non-equilibrium thermodynamic theory:
othertheories, inparticular theso-calledrationalthermodynamics,haveachieved some
valuable results.To reconcile theclassical andtherationalpoints ofview, itwould be
of interest to have a theory able to provide a sufficiently wide ground for discussion,
thus making their common points evident and their main differences understandable.
Extendedirreversiblethermodynamicsisapromisingcandidate.
Extended irreversible thermodynamics received a strong impetus in the past
decade. Besides the classical thermodynamic variables, this theory introduces as new
independent variables the dissipative fluxes and aims to obtain for them evolution
equations compatible withthesecondlawofthermodynamics.The centralquantity isa
generalised non-equilibrium entropy,depending on both the conserved variables and
the fluxes, which sheds new light on the content ofthe second law. This generalised
theory is corroborated from a microscopic point of view by the kinetic theory, non
equilibrium information theory and other formulations of non-equilibrium statistical
mechanics.
The purpose of this book is to provide an introduction to the foundations of
extended irreversible thermodynamics, todiscussthemainresults andtopresent some
of its applications. After more than twenty years of research and several hundreds of
papers published by many groups in several countries we feel such a book is sorely
needed.Guided bytheaimtobeasillustrativeandpedagogicalaspossible,arelatively
PrefacetotheFirstEdition IX
simple formulation of the theory is presented, but this is nevertheless more than
sufficient for the description of several phenomena not accessible to the classical
theory.The various topics treatedin this bookrangefrom thermal waves and phonon
hydrodynamics to material and electrical transport, from ultrasound propagation and
generalised hydrodynamics to rheology,fromkinetic theory tocosmology.Of course,
other formulations of extended thermodynamics and other kinds of applications are
possible. They are likely to arise in the near future. We hope that this book will be
useful in providing a generalview of present achievementsand in stimulating future
research.
We areverypleased toacknowledgemanystimulatingdiscussions with ourcol
leagues Carlos Perez-Garcfa,Josep-EnricLlebot,DiegoPav6n,Jose-Miguel Rubfand
Joseph Lambennontfor morethanfifteenyearsofjoint research, andalso with many
other colleagues from the different groups which have devoted their attention to
extended irreversible thermodynamics.We also acknowledge the financial support of
the Comisi6n Asesora para la Investigaci6nCientfficayTecnica of the Spanish Gov
ernment during the years 1979-1986 under grants 3913n9 and 2389/83, and of the
Direcci6n General de Investigaci6n Cientffica y Tecnica of the Spanish Ministry of
Education, under grants PB86-0287, PB89-0290, and PB90-0676. The collaboration
between our groups in Bellaterra and Liege has been made economically possible
becauseoftheNATOgrant0355/83.
March 1993
DavidJou
Jose Casas-Vdzquez
GeorgyLebon
Contents
PartI. General Theory
1 Classicaland Rational Formulations
ofNon-equilibriumThermodynamics 3
1.1 TheGeneral BalanceLawsofContinuumPhysics 4
1.2 The Law ofBalanceofEntropy .................................. 13
1.3 Classical Irreversible Thermodynamics ............................ 15
1.4 Rational Thermodynamics ...................................... 24
Problems 33
2 ExtendedIrreversibleThermodynamics:
EvolutionEquations 39
2.1 Heat Conduction 40
2.2 One-componentViscousFluid................................... 47
2.3 TheGeneralisedEntropyFluxandEntropyProduction 49
2.4 LinearizedEvolution EquationsoftheFluxes ....................... 52
2.5 Rational ExtendedThermodynamics .. ............................ 54
2.6 Some Comments andPerspectives. ............. .... 65
2.7 Entropy EvolutioninanIsolatedSystem:Anlllustrative Example. ...... 66
Problems 70
3 ExtendedIrreversibleThermodynamics:
Non-equilibriumEquations ofState........................... 73
3.1 Physical Interpretation oftheNon-equilibriumEntropy 74
3.2 Non-equilibriumEquationsof State:Temperature ............ 77
3.3 Non-equilibriumEquations ofState:Thermodynamic Pressure.......... 83
3.4 Convexity Requirements andStability 87
Problems 92
