LEADER 05696nam 2200721 450 001 9910465345203321 005 20210423220939.0 010 $a0-691-14747-7 010 $a1-4008-6522-0 024 7 $a10.1515/9781400865222 035 $a(CKB)3710000000222322 035 $a(EBL)1756200 035 $a(OCoLC)888349118 035 $a(SSID)ssj0001385066 035 $a(PQKBManifestationID)11796997 035 $a(PQKBTitleCode)TC0001385066 035 $a(PQKBWorkID)11330334 035 $a(PQKB)10932197 035 $a(MiAaPQ)EBC1756200 035 $a(DE-B1597)448028 035 $a(OCoLC)891400524 035 $a(OCoLC)979755922 035 $a(OCoLC)984687055 035 $a(OCoLC)987927761 035 $a(OCoLC)992454375 035 $a(OCoLC)999369723 035 $a(DE-B1597)9781400865222 035 $a(Au-PeEL)EBL1756200 035 $a(CaPaEBR)ebr10910143 035 $a(CaONFJC)MIL637573 035 $a(EXLCZ)993710000000222322 100 $a20140829h20032003 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 00$aEntropy /$fAndreas Greven, Gerhard Keller, Gerald Warnecke, editors 210 1$aPrinceton, New Jersey ;$aOxfordshire, England :$cPrinceton University Press,$d2003. 210 4$dİ2003 215 $a1 online resource (376 p.) 225 1 $aPrinceton Series in Applied Mathematics 300 $aDescription based upon print version of record. 311 $a1-322-06322-2 311 $a0-691-11338-6 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tPreface --$tList of Contributors --$tChapter One. Introduction /$rGreven, Andreas / Keller, Gerhard / Warnecke, Gerald --$tPART 1. Fundamental Concepts --$tChapter Two. Entropy: a Subtle Concept in Thermodynamics /$rMüller, Ingo --$tChapter Three. Probabilistic Aspects of Entropy /$rGeorgii, Hans-Otto --$tPART 2. Entropy in Thermodynamics --$tChapter Four. Phenomenological Thermodynamics and Entropy Principles /$rHutter, Kolumban / Wang, Yongqi --$tChapter Five. Entropy in Nonequilibrium /$rMüller, Ingo --$tChapter Six. Entropy for Hyperbolic Conservation Laws /$rDafermos, C. M. --$tChapter Seven. Irreversibility and the Second Law of Thermodynamics /$rUffink, Jos --$tChapter Eight. The Entropy of Classical Thermodynamics /$rLieb, Elliott H. / Yngvason, Jakob --$tPART 3. Entropy in Stochastic Processes --$tChapter Nine. Large Deviations and Entropy /$rVaradhan, S. R. S. --$tChapter Ten. Relative Entropy for Random Motion in a Random Medium /$rHollander, F. den --$tChapter Eleven. Metastability and Entropy /$rOlivieri, E. --$tChapter Twelve. Entropy Production in Driven Spatially Extended Systems /$rMaes, Christian --$tChapter Thirteen. Entropy: a Dialogue --$tPART 4. Entropy and Information --$tChapter Fourteen. Classical and Quantum Entropies: Dynamics and Information /$rBenatti, Fabio --$tChapter Fifteen. Complexity and Information in Data /$rRissanen, J. --$tChapter Sixteen. Entropy in Dynamical Systems --$tChapter Seventeen. Entropy in Ergodic Theory --$tCombined References --$tIndex 330 $aThe concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems. Two main views developed: the macroscopic view formulated originally by Carnot, Clausius, Gibbs, Planck, and Caratheodory and the microscopic approach associated with Boltzmann and Maxwell. Since then both approaches have made possible deep insights into the nature and behavior of thermodynamic and other microscopically unpredictable processes. However, the mathematical tools used have later developed independently of their original physical background and have led to a plethora of methods and differing conventions. The aim of this book is to identify the unifying threads by providing surveys of the uses and concepts of entropy in diverse areas of mathematics and the physical sciences. Two major threads, emphasized throughout the book, are variational principles and Ljapunov functionals. The book starts by providing basic concepts and terminology, illustrated by examples from both the macroscopic and microscopic lines of thought. In-depth surveys covering the macroscopic, microscopic and probabilistic approaches follow. Part I gives a basic introduction from the views of thermodynamics and probability theory. Part II collects surveys that look at the macroscopic approach of continuum mechanics and physics. Part III deals with the microscopic approach exposing the role of entropy as a concept in probability theory, namely in the analysis of the large time behavior of stochastic processes and in the study of qualitative properties of models in statistical physics. Finally in Part IV applications in dynamical systems, ergodic and information theory are presented. The chapters were written to provide as cohesive an account as possible, making the book accessible to a wide range of graduate students and researchers. Any scientist dealing with systems that exhibit entropy will find the book an invaluable aid to their understanding. 410 0$aPrinceton series in applied mathematics. 606 $aEntropy 608 $aElectronic books. 615 0$aEntropy. 676 $a536/.73 702 $aGreven$b Andreas$f1953- 702 $aKeller$b Gerhard$f1954- 702 $aWarnecke$b Gerald$f1956- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465345203321 996 $aEntropy$91920374 997 $aUNINA