Lecture Notes in Physics Dynamics of Dissipation, Book 597, (Paperback)

The present volume contains expanded and substantially reworked records of invitedlecturesdeliveredduringthe38thKarpaczWinterSchoolofTheoretical Physics on Dynamical Semigroups: Dissipation, Chaos, Quanta, which took placeinLadek, Zdr oj, (Poland)intheperiod6 15February2002. Themainpurposeoftheschoolwastocreateaplatformfortheconfrontation ofviewpointsandresearchmethodologiesrepresentedbytwogroupsofexperts actually working in the very same area of theoretical physics. This situation is quite distinct in non-equilibrium statistical physics of open systems, where classicalandquantumaspectsareaddressedseparatelybymeansofverydi?erent andevenincompatibleformaltools. TheschooltopicsselectionbytheLecturersreads: dissipativedynamicsand chaoticbehaviour, modelsofenvironment systemcouplingandmodelsofth- mostats;non-equilibriumstatisticalmechanicsandfarfromequilibriumphen- ena;quantumopensystems, decoherenceandlinkstoquantumchaos;quantum andclassicalapplicationsofMarkovsemigroupsandthevalidityofMarkovian approximations. Theorganizingprincipleforthewholeendeavourwastheissueofthedyn- ics of open systems and more speci?cally thedynamics of dissipation. Since this research area is extremely broad and varied, no single book can cover all importantdevelopments. Therefore, linkswithdynamicalchaoswerechosento representasupplementaryconstraint. Theprogrammeoftheschoolandits?naloutcomeintheformofthepresent volumehasbeenshapedwiththehelpofthescienti?ccommitteecomprising: R. Alicki, Ph. Blanchard, J. R. Dorfman, G. Gallavotti, P. Gaspard, I. Guarneri, ? F. Haake, M. Kus, A. Lasota, B. Zegarlinski and K. Zyczkowski. Some of the committeememberstookchargeoflecturingtoo. Weconveyourthankstoall ofthem. Wewouldliketoexpresswordsofgratitudetomembersofthelocalorgan- ingcommittee, W. Ceg laandP. Lugiewicz, fortheirhelp. Specialthanksmust beextendedtoMrsAnnaJadczykforherhelpatvariousstagesoftheschool organizationandthecompetenteditorialassistance. Theschoolwas?nanciallysupportedbytheUniversityofWroc law, Univ- sityofZielonaG ora, PolishMinistryofEducation, PolishAcademyofSciences, FoundationfortheKarpaczWinterSchoolofTheoreticalPhysicsandthe- nationfromtheDrWilhelmHeinrichHeraeusundElseHeraeusStiftung. Wrocla wandZielonaG ora, Poland PiotrGarbaczewski June2002 RobertOlkiewicz TableofContents Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 ChapterI NonequilibriumDynamics SomeRecentAdvancesinClassicalStatisticalMechanics E. G. D. Cohen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 DeterministicThermostatsandFluctuationRelations L. Rondoni. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 WhatIstheMicroscopicResponseofaSystem DrivenFarFromEquilibrium? C. Jarzynski. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Non-equilibriumStatisticalMechanics ofClassicalandQuantumSystems D. Kusnezov, E. Lutz, K. Aoki. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 ChapterII DynamicsofRelaxationandChaoticBehaviour DynamicalTheoryofRelaxation inClassicalandQuantumSystems P. Gaspard. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 RelaxationandNoiseinChaoticSystems S. Fishman, S. Rahav. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 FractalStructuresinthePhaseSpace ofSimpleChaoticSystemswithTransport J. R. Dorfman. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 ChapterIII DynamicalSemigroups MarkovSemigroupsandTheirApplications R. Rudnicki, K. Pichor, M. Tyran-Kaminska . . . . . . . . . . . . . . . . . . . . . . . . . 215 VIII TableofContents InvitationtoQuantumDynamicalSemigroups R. Alicki. . . . . . . . . . . . . . . .