Special Volume in Memory of Ilya Prigogine: Advances in Chemical Physics, Volume 135

334 Pages·2007·19.068 MB·English

by  Stuart A. Rice (ed.)

SPECIAL VOLUME IN
MEMORY OF ILYA
PRIGOGINE
ADVANCES IN CHEMICAL PHYSICS
VOLUME135

SPECIAL VOLUME IN
MEMORY OF ILYA
PRIGOGINE
ADVANCESINCHEMICALPHYSICS
VOLUME135
Edited by
STUARTA. RICE
DepartmentofChemistry
and
TheJamesFranckInstitute
TheUniversityofChicago
Chicago,Illinois
AN INTERSCIENCE PUBLICATION
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CONTRIBUTORS TO VOLUME 135
A. ARNEODO, Laboratoire Joliot-Curie et Laboratoire de Physiques, Ecole
Normale Supe´rieure de Lyon, 69364 Lyon Cedex 07, France
B. AUDIT, Laboratoire Joliet-Curie et Laboratoire de Physique, CNRS, Ecole
Normale Supe´rieure de Lyon, 69364 Lyon Cedex 07, France
RADU BALESCU*, Association Euratom—Belgian State for Fusion, Universite´
Libre de Bruxelles, B-1050 Brussels, Belgium
E. B. BRODIE OF BRODIE, Laboratoire Joliet-Curie et Laboratoire de Physique,
CNRS, Ecole Normale Supe´rieure de Lyon, 6934 Lyon Cedex 07, France
Y. D’AUBENTON-CARAFA, Centre de Ge´ne´tique Mole´culaire, CNRS, 91198 Gif-
sur-Yvette, France
PIERRE GASPARD, Center for Nonlinear Phenomena and Complex Systems,
Universite´ Libre de Bruxelles, B-1050 Brussels, Belgium
ALBERTGOLDBETER,ServicedeChimie,Physique,etBiologieThe´orique,Faculte´
desSciences,Universite´ LibredeBruxelles,B-1050Bruxelles,Belgium
S. NICOLAY, Laboratoire Joliet-Curie et Laboratoire de Physique, CNRS, Ecole
Normale Supe´rieure de Lyon, 6934 Lyon Cedex 07, France
GONZOLO ORDONEZ, Center for Studies in Statistical Mechanics and Complex
Systems, The University of Texas, Austin, Texas 78712, USA; and
International Solvay Institutes for Physics and Chemistry, CP231, B-1050
Brussels, Belgium. Present Address: Butler University, Indianapolis,
Indiana 46208, USA
TOMIO PETROSKY, Center for Studies in Statistical Mechanics and Complex
Systems, The University of Texas, Austin, Texas 78712 USA; and
International Solvay Institutes for Physics and Chemistry, CP231, B-1050
Brussels, Belgium
YVES POMEAU, Laboratoire de Physique Statistique de L’Ecole Normale
Supe´rieure, 75231 Cedex 05, France. Present Address: Department of
Mathematics, The University of Arizona, Tucson, Arizona 85721, USA
ILYA PRIGOGINEy, Center for Studies in Statistical Mechanics and Complex
Systems, The University of Texas, Austin, Texas 78712, USA; and
*Deceased.
yDeceased.
v
vi contributors to volume 135
International solvay Institutes for Physics and Chemistry, CP231, B-1050
Brussels, Belgium
JOHN ROSS, Stanford University, Department of Chemistry, Stanford, California
94305, USA
P. ST. JEAN, Laboratoire Joliet-Curie et Laboratoire de Physique, CNRS, Ecole
Normale Supe´rieure de Lyon, 6934 Lyon Cedex 07, France
C. THERMES, Centre de Ge´ne´tique Moleculaire, CNRS, 91198 Gif-sur-Yvette,
France
M. TOUCHON, Centre de Ge´ne´tique Moleculaire, CNRS, 91198 Gif-sur-Yvette,
France
C. VAILLANT, Laboratoire Statistique et Ge´nome, 91000 Evry, France
CHRISTIANVANDENBROECK,HasseltUniversity,Dept.WN1,B-3590Diepenbeek,
Belgium
MARCEL VLAD, Department of Chemistry, Stanford University, Stanford,
California 94305, USA; and Institute of Mathematical Statistics and
Applied Mathematics, Casa Academiei Romane, 76100
INTRODUCTION
Fewofuscananylongerkeepupwiththefloodofscientificliterature,even
in specialized subfields. Any attempt to do more and be broadly educated
with respect to a large domain of science has the appearance of tilting at
windmills.Yetthesynthesisofideasdrawnfromdifferentsubjectsintonew,
powerful, general concepts is as valuable as ever, and the desire to remain
educated persists in all scientists. This series, Advances in Chemical
Physics,is devoted tohelpingthereader obtain generalinformationabouta
wide variety of topics in chemical physics, a field that we interpret very
broadly. Our intent is to have experts present comprehensive analyses of
subjects of interest and to encourage the expression of individual points of
view. We hope that this approach to the presentation of an overview of a
subjectwillbothstimulatenewresearchandserveasapersonalizedlearning
text for beginners in a field.
STUARTA. RICE
vii
ACKNOWLEDGMENTS
The Symposium In Memoriam Ilya Prigogine on‘‘Time, Irreversibility and
Self-Organization’’ was held by the International Solvay Institutes for
Physics and Chemistry at the University of Brussels on December 2–3,
2004.
ThisSymposiumwas madepossiblebythesponsorshipsoftheEuropean
Commission,oftheFondsNationaldelaRechercheScientifique(FNRS),of
the Nationale Fonds voor Wetenschappelijk Onderzoek (NFWO), of the
Belgian National Lottery, of the ‘‘Communaute´ Franaise de Belgique,’’ and
of the ‘‘Hotel Me´tropole,’’ which are gratefully acknowledged.
PROF. RENE LEFEVER
Universite´ Libre de Bruxelles Belgium
ix
CONTENTS
ILYA PRIGOGINE: HIS LIFE, HIS WORK 1
By Radu Balescu
TIME ASYMMETRYIN NONEQUILIBRIUM STATISTICAL MECHANICS 83
By Pierre Gaspard
QUANTUMAND CLASSICAL DYNAMICSOF NONINTEGRABLE SYSTEMS 135
By Ilya Prigogine, Tomio Petrosky, and Gonzolo Ordonez
STATISTICAL MECHANICSOFA GRAVITATIONAL PLASMA 153
By Yves Pomeau
INVERSE PROBLEMSFOR REACTION-DIFFUSION SYSTEMS
WITH APPLICATIONTO GEOGRAPHICAL POPULATION GENETICS 173
By Marcel O. Vlad and John Ross
CARNOT EFFICIENCY REVISITED 189
By C. Van den Broeck
DNA IN CHROMATIN: FROM GENOME-WIDE SEQUENCE ANALYSIS
TOTHE MODELINGOF REPLICATION IN MAMMALS 203
By A. Arneodo, B. Audit, E. B. Brodie of Brodie, S. Nicolay,
P. St. Jean, Y. d’Aubenton-Carafa, C. Thermes, M. Touchon,
and C. Vaillant
BIOLOGICAL RHYTHMSAS TEMPORAL DISSIPATIVE STRUCTURES 253
By Albert Goldbeter
Author Index 297
Subject Index 311
xi
group
backward semigroup forward semigroup
>t
A
<
<A>
eq
-10 -5 0 5 10
t
Figure 5. Timeevolutionofthestatisticalaverage(51)accordingtotheexpansion(52)ofthe
forwardsemigroupvalidfort > 0andtheexpansion(35)ofthebackwardsemigroupvalidfort < 0.
1.2
1
0.8
P(ω) ~ exp(−ht)
0.6
0.4
P(ωR) ~ exp(−hRt) exp(∆iS/kB)
0.2
0
0 5 10 15 20
t = n τ
Figure15. Diagramshowingtheprobabilityofapathandtheprobabilityofthecorresponding
timereversalasafunctionofthenumbernoftimeintervalst,illustratingtheformula(101).(cid:1)S
i
denotestheentropyproductionduringthewholedurationnt.
6 1 2
5
3
4
hR
3
2 ∆ iS
1
h
0 0.2 0.4 0.6 0.8 1
a
1 2 eq
3
Figure18. Thedynamicalentropies(126)and(127)aswellastheentropyproduction(128)forthe
three-stateMarkovchaindefinedbythematrix(125)oftransitionprobabilitiesversustheparametera.
Theequilibriumcorrespondstothevaluea¼2=3.Theprocessisperfectlycyclicata¼0wherethepath
is...123123123123...andtheKolmogorov–Sinaientropyhvanishesasaconsequence.