Challenges to the Second Law of Thermodynamics Theory and Experiment Vladislav Capek and Daniel P.Sheehan Springer Fundamental Theories of Physics
Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification,Development and Application Editor: ALWYN VAN DER MERWE,University of Denver,U.S.A. Editorial Advisory Board: JAMES T.CUSHING,University of Notre Dame,U.S.A. GIANCARLO GHIRARDI,University of Trieste,Italy LAWRENCE P.HORWITZ,Tel-Aviv University,Israel BRIAN D.JOSEPHSON,University of Cambridge,U.K. CLIVE KILMISTER,University of London,U.K. PEKKA J.LAHTI,University of Turku,Finland ASHER PERES,Israel Institute of Technology,Israel EDUARD PRUGOVECKI,University of Toronto,Canada TONY SUDBURY,University of York,U.K. HANS-JURGEN TREDER,Zentralinstitut fuir Astrophysik der Akademie der Wissenschaften,Germany Volume 146
Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: JAMES T. CUSHING, University of Notre Dame, U.S.A. GIANCARLO GHIRARDI, University of Trieste, Italy LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada TONY SUDBURY, University of York, U.K. HANS-JÜRGEN TREDER, Zentralinstitut für Astrophysik der Akademie der Wissenschaften, Germany Volume 146
Challenges to the Second Law of Thermodynamics Theory and Experiment By Vladislav Capek Charles University, Prague,Czech Republic and Daniel P.Sheehan University of San Diego, San Diego,California,U.S.A. Springer
Second Law of Thermodynamics Theory and Experiment By Vladislav Prague, Czech Republic and Daniel P. Sheehan University of San Diego, Challenges to the Charles University, San Diego, California, U.S.A. ýápek
Contents Preface xiii Acknowledgements xvi 1 Entropy and the Second Law 1.1 Early Thermodynamics..................................1 1.2 The Second Law:Twenty-One Formulations .............3 1.3 Entropy:Twenty-One Varieties ........................ 13 1.4 Nonequilibrium Entropy ............................... 23 1.5 Entropy and the Second Law:Discussion .............. 26 1.6 Zeroth and Third Laws of Thermodynamics ............27 References 30 2 Challenges (1870-1980) 2.1 Maxwell's Demon and Other Victorian Devils ..........35 2.2 Exorcising Demons .................................... 39 2.2.1 Smoluchowski and Brillouin ......................39 2.2.2 Szilard Engine ................................... 40 2.2.3 Self-Rectifying Diodes ........................... 41 2.3 Inviolability Arguments............. .42 2.3.1 Early Classical Arguments..... 43 2.3.2 Modern Classical Arguments ............. 44 2.4 Candidate Second Law Challenges ............ 48 References 51 3 Modern Quantum Challenges:Theory 3.1 Prolegomenon..·· 53
Contents Preface xiii Acknowledgements xvi 1 Entropy and the Second Law 1.1 Early Thermodynamics .................................. 1 1.2 The Second Law: Twenty-One Formulations . . . . . . . . . . . . . . 3 1.3 Entropy: Twenty-One Varieties . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4 Nonequilibrium Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.5 Entropy and the Second Law: Discussion . . . . . . . . . . . . . . . 26 1.6 Zeroth and Third Laws of Thermodynamics . . . . . . . . . . . . . 27 References 30 2 Challenges (1870-1980) 2.1 Maxwell’s Demon and Other Victorian Devils . . . . . . . . . . . 35 2.2 Exorcising Demons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.2.1 Smoluchowski and Brillouin . . . . . . . . . . . . . . . . . . . . . . . 39 2.2.2 Szilard Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.2.3 Self-Rectifying Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.3 Inviolability Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.3.1 Early Classical Arguments . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.3.2 Modern Classical Arguments . . . . . . . . . . . . . . . . . . . . . 44 2.4 Candidate Second Law Challenges . . . . . . . . . . . . . . . . . . . . . . 48 References 51 3 Modern Quantum Challenges: Theory 3.1 Prolegomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
viii Challenges to the Second Law 3.2 Thermodynamic Limit and Weak Coupling ..............55 3.3 Beyond Weak Coupling:Quantum Correlations......... 67 3.4 Allahverdyan and Nieuwenhuizen Theorem .............69 3.5 Scaling and Beyond ....................................71 3.6 Quantum Kinetic and Non-Kinetic Models .............75 3.6.1 Fish-Trap Model..................................76 3.6.2 Semi-Classical Fish-Trap Model................... 83 3.6.3 Periodic Fish-Trap Model.........................87 3.6.4 Sewing Machine Model .......................... 91 3.6.5 Single Phonon Mode Model......................97 3.6.6 Phonon Continuum Model ......................101 3.6.7 Exciton Diffusion Model ........................101 3.6.8 Plasma Heat Pump Model....................... 102 3.7 Disputed Quantum Models ........................... 105 3.7.1 Porto Model ............. 106 3.7.2 Novotny........ 106 3.8 Kinetics in the DC Limit ................ 106 3.8.1TC-GME and Mori............107 3.8.2 TCL-GME and Tokuyama-Mori ..................110 3.9 Theoretical Summary..................................111 References 113 4 Low-Temperature Experiments and Proposals 4.1 Introduction...................... 117 4.2 Superconductivity .......... 117 4.2.1 Introduction ........ 117 4.2.2 Magnetocaloric Effect 119 4.2.3 Little-Parks Effect .................... 120 4.3 Keefe CMCE Engine ...... 121 4.31 Theory..… 121 4.3.2 Discussion.…· 124 4.4 Nikulov Inhomogeneous Loop ....... 125 4.4.1 Quantum Force ........... ...125 4.4.2 Inhomogeneous Superconducting Loop ...........127 4.4.3 Experiments ....... .129 4.4.3.1 Series I...... 129 4.4.3.2 Series II...... 131 4.4.4 Discussion ...... 134
viii 3.2 Thermodynamic Limit and Weak Coupling . . . . . . . . . . . . . . 55 3.3 Beyond Weak Coupling: Quantum Correlations . . . . . . . . . 67 3.4 Allahverdyan and Nieuwenhuizen Theorem . . . . . . . . . . . . . . 69 3.5 Scaling and Beyond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.6 Quantum Kinetic and Non-Kinetic Models . . . . . . . . . . . . . . 75 3.6.1 Fish-Trap Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.6.2 Semi-Classical Fish-Trap Model . . . . . . . . . . . . . . . . . . . 83 3.6.3 Periodic Fish-Trap Model . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.6.4 Sewing Machine Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.6.5 Single Phonon Mode Model . . . . . . . . . . . . . . . . . . . . . . 97 3.6.6 Phonon Continuum Model . . . . . . . . . . . . . . . . . . . . . . . 101 3.6.7 Exciton Diffusion Model . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.6.8 Plasma Heat Pump Model . . . . . . . . . . . . . . . . . . . . . . . 102 3.7 Disputed Quantum Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.7.1 Porto Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.7.2 Novotn´y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.8 Kinetics in the DC Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.8.1 TC-GME and Mori . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.8.2 TCL-GME and Tokuyama-Mori . . . . . . . . . . . . . . . . . . 110 3.9 Theoretical Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 References 113 4 Low-Temperature Experiments and Proposals 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.2 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.2.2 Magnetocaloric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.2.3 Little-Parks Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.3 Keefe CMCE Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.4 Nikulov Inhomogeneous Loop . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.4.1 Quantum Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.4.2 Inhomogeneous Superconducting Loop . . . . . . . . . . . 127 4.4.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.4.3.1 Series I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.4.3.2 Series II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Challenges to the Second Law