《热力学 Thermodynamics（I）》课程教学资源：阅读书籍文献_Challenges to the Second Law of Thermodynamics

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

Contents ix 4.5 Bose-Einstein Condensation and the Second Law ......134 4.6 Quantum Coherence and Entanglement................135 4.6.1 Introduction..............135 4.6.2 Spin-Boson Model...............................136 4.6.3 Mesoscopic LC Circuit Model...................137 4.6.4 Experimental Outlook ...........................139 References 141 5 Modern Classical Challenges 5.1 Introduction...… ...145 5.2 Gordon Membrane Models ............... 146 5.2.1 Introduction.....................................146 5.2.2 Membrane Engine ...............................147 5.2.3 Molecular Trapdoor Model ..................... 150 5.2.4 Molecular Rotor Model..........................152 5.2.5 Discussion..................... 154 5.3 Denur Challenges .............. 154 5.3.1 Introduction.....................................154 5.3.2 Dopper Demon..................................155 5.3.3 Ratchet and Pawl Engine .......................156 5.4 Crosignani-Di Porto Adiabatic Piston.................. 159 5.4.1 Theory ............... 159 5.4.2 Discussion ........ 163 5.5 Trupp Electrocaloric Cycle 164 5.5.1 Theory .............. 164 5.5.2 Experiment ...... 167 5.5.3 Discussion ........ 168 5.6 Liboff Tri-Channel ......... 169 5.7 Thermodynamic Gas Cycles 171 References 172 6 Gravitational Challenges 6.1 Introduction.… ...175 6.2 Asymmetric Gravitator Model................. .177 6.2.1 Introduction…… .177 6.2.2 Model Specifications ...... ….178 6.2.3 One-Dimensional Analysis ........................180 6.2.4 Numerical Simulations ................. ...183

Contents ix 4.5 Bose-Einstein Condensation and the Second Law . . . . . . . 134 4.6 Quantum Coherence and Entanglement . . . . . . . . . . . . . . . . 135 4.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.6.2 Spin-Boson Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 4.6.3 Mesoscopic LC Circuit Model . . . . . . . . . . . . . . . . . . . 137 4.6.4 Experimental Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 References 141 5 Modern Classical Challenges 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5.2 Gordon Membrane Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.2.2 Membrane Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 5.2.3 Molecular Trapdoor Model . . . . . . . . . . . . . . . . . . . . . . 150 5.2.4 Molecular Rotor Model . . . . . . . . . . . . . . . . . . . . . . . . . . 152 5.2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 5.3 Denur Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 5.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 5.3.2 Dopper Demon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 5.3.3 Ratchet and Pawl Engine . . . . . . . . . . . . . . . . . . . . . . . . 156 5.4 Crosignani-Di Porto Adiabatic Piston . . . . . . . . . . . . . . . . . . 159 5.4.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 5.4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 5.5 Trupp Electrocaloric Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 5.5.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 5.5.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 5.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 5.6 Liboff Tri-Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 5.7 Thermodynamic Gas Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 References 172 6 Gravitational Challenges 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175 6.2 Asymmetric Gravitator Model . . . . . . . . . . . . . . . . . . . . . . . . . .177 6.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 6.2.2 Model Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 6.2.3 One-Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . 180 6.2.4 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

X Challenges to the Second Law 6.2.4.1 Velocity Distributions .......................184 6.2.4.2 Phase Space Portraits ......................187 6.2.4.3 Gas-Gravitator Dynamics ...................192 6.2.5 Wheeler Resolution ..................... ..197 6.2.6 Laboratory Experiments........·.· ...198 6.3 Loschmidt Gravito-Thermal Effect......................202 6.3.1 Graff Experiments...............................203 6.3.2 Trupp Experiments................206 References 207 7 Chemical Nonequilibrium Steady States 7.1 Introduction..................... 211 7.2 Chemical Paradox and Detailed Balance .............. 214 7.3 Pressure Gradients and Reactions Rates .............. 218 7.4 Numerical Simulations ................................224 7.5 Laboratory Experiments·…· 227 7.5.1 Introduction .................................... 227 7.5.2 Apparatus and Protocol......................... 228 7.5.3 Results and Interpretation ...................... 230 7.6 Discussion and Outlook ............................... 233 References 237 8 Plasma Paradoxes 8.1 Introduction ....... 239 8.2 Plasma I System...…… 240 82.1The0y 240 8.2.2 Experiment......................................244 8.2.2.1 Apparatus and Protocol ....................244 8.2.2.2 Results and Interpretation .................247 8.3 Plasma II System ................ 251 8.3.1 Theory.… 251 8.3.2 Experiment ................. 258 8.3.2.1 Apparatus and Protocol .............. 258 8.3.2.2 Results and Interpretation ................ 260 8.4 Jones and Cruden Criticisms ......................... 262 References 266

x 6.2.4.1 Velocity Distributions . . . . . . . . . . . . . . . . . . . . . . .184 6.2.4.2 Phase Space Portraits . . . . . . . . . . . . . . . . . . . . . . 187 6.2.4.3 Gas-Gravitator Dynamics . . . . . . . . . . . . . . . . . . . 192 6.2.5 Wheeler Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.2.6 Laboratory Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 198 6.3 Loschmidt Gravito-Thermal Effect . . . . . . . . . . . . . . . . . . . . . . 202 6.3.1 Gr¨aff Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 6.3.2 Trupp Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .206 References 207 7 Chemical Nonequilibrium Steady States 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 7.2 Chemical Paradox and Detailed Balance . . . . . . . . . . . . . . . 214 7.3 Pressure Gradients and Reactions Rates . . . . . . . . . . . . . . . 218 7.4 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 7.5 Laboratory Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 7.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 7.5.2 Apparatus and Protocol . . . . . . . . . . . . . . . . . . . . . . . . . 228 7.5.3 Results and Interpretation . . . . . . . . . . . . . . . . . . . . . . . 230 7.6 Discussion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 References 237 8 Plasma Paradoxes 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 8.2 Plasma I System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 8.2.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 8.2.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 8.2.2.1 Apparatus and Protocol . . . . . . . . . . . . . . . . . . . . 244 8.2.2.2 Results and Interpretation . . . . . . . . . . . . . . . . . 247 8.3 Plasma II System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 8.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 8.3.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 8.3.2.1 Apparatus and Protocol . . . . . . . . . . . . . . . . . . . . 258 8.3.2.2 Results and Interpretation . . . . . . . . . . . . . . . . . 260 8.4 Jones and Cruden Criticisms . . . . . . . . . . . . . . . . . . . . . . . . . . 262 References 266 Challenges to the Second Law

Contents 灯 9 MEMS/NEMS Devices 9.1 Introduction .......... 267 9.2 Thermal Capacitors ........... 268 9.2.1 Theory268 9.2.2 Numerical Simulations .......................... 273 9.3 Linear Electrostatic Motor (LEM)..................... 277 9.3.1 Theory… 277 9.3.2 Numerical Simulations .......................... 284 9.3.3 Practicality and Scaling ........................ 286 9.4 Hammer-Anvil Model......... 291 9.4.1 Theory .............. 291 9.4.2 Operational Criteria ... 295 9.4.3 Numerical Simulations ............... 298 9.5 Experimental Prospects ..... 300 References 301 10 Special Topics 10.1 Rubrics for Classical Challenges .......................303 10.1.1 Macroscopic Potential Gradients (MPG)........304 10.1.2 Zhang-Zhang Flows.............................307 10.2 Thermosynthetic Life ......... .308 10.2.1 Introduction........ ...308 10.2.2 Theory…… ....312 10.2.3 Experimental Search .............. ..318 10.3 Physical Eschatology ..................................319 10.3.1 Introduction...................319 10.3.2 Cosmic Entropy Production.....................322 10.3.3 Life in the Far Future ...........................324 10.4 The Second Law Mystique ............................327 References 331 Color Plates 335 Index 343

Contents xi 9 MEMS/NEMS Devices 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 9.2 Thermal Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 9.2.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 9.2.2 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 9.3 Linear Electrostatic Motor (LEM) . . . . . . . . . . . . . . . . . . . . . 277 9.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 9.3.2 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 9.3.3 Practicality and Scaling . . . . . . . . . . . . . . . . . . . . . . . . . 286 9.4 Hammer-Anvil Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 9.4.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 9.4.2 Operational Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 9.4.3 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 9.5 Experimental Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 References 301 10 Special Topics 10.1 Rubrics for Classical Challenges . . . . . . . . . . . . . . . . . . . . . . . 303 10.1.1 Macroscopic Potential Gradients (MPG) . . . . . . . . 304 10.1.2 Zhang-Zhang Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 10.2 Thermosynthetic Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .308 10.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 10.2.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 10.2.3 Experimental Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 10.3 Physical Eschatology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 10.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 10.3.2 Cosmic Entropy Production . . . . . . . . . . . . . . . . . . . . . 322 10.3.3 Life in the Far Future . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 10.4 The Second Law Mystique . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 References 331 Color Plates 335 Index 343

Preface The advance of scientific thought in ways resembles biological and geologic transformation:long periods of gradual change punctuated by episodes of radical upheaval.Twentieth century physics witnessed at least three major shifts- relativity,quantum mechanics and chaos theory-as well many lesser ones.Now, early in the 21st,another shift appears imminent,this one involving the second law of thermodynamics. Over the last 20 years the absolute status of the second law has come under increased scrutiny,more than during any other period its 180-year history.Since the early 1980's,roughly 50 papers representing over 20 challenges have appeared in the refereed scientific literature.In July 2002,the first conference on its status was convened at the University of San Diego,attended by 120 researchers from 25 countries (QLSL2002)[1].In 2003,the second edition of Leff's and Rex's classic anthology on Maxwell demons appeared [2],further raising interest in this emerging field.In 2004,the mainstream scientific journal Entropy published a special edition devoted to second law challenges [3].And,in July 2004,an echo of QLSL2002 was held in Prague,Czech Republic [4. Modern second law challenges began in the early 1980's with the theoretical proposals of Gordon and Denur.Starting in the mid-1990's,several proposals for experimentally testable challenges were advanced by Sheehan,et al.By the late 1990's and early 2000's,a rapid succession of theoretical quantum mechanical challenges were being advanced by Capek,et al.,Allahverdyan,Nieuwenhuizen, et al.,classical challenges by Liboff,Crosignani and Di Porto,as well as more experimentally-based proposals by Nikulov,Keefe,Trupp,Graff,and others. The breadth and depth of recent challenges are remarkable.They span three orders of magnitude in temperature,twelve orders of magnitude in size;they are manifest in condensed matter,plasma,gravitational,chemical,and biological physics;they cross classical and quantum mechanical boundaries.Several have strong corroborative experimental support and laboratory tests attempting bona fide violation are on the horizon.Considered en masse,the second law's absolute status can no longer be taken for granted,nor can challenges to it be casually dismissed. This monograph is the first to examine modern challenges to the second law. For more than a century this field has lain fallow and beyond the pale of legitimate scientific inquiry due both to a dearth of scientific results and to a surfeit of peer pressure against such inquiry.It is remarkable that 20h century physics, which embraced several radical paradigm shifts,was unwilling to wrestle with this remnant of 19th century physics,whose foundations were admittedly suspect and largely unmodified by the discoveries of the succeeding century.This failure is due in part to the many strong imprimaturs placed on it by prominent scientists like Planck,Eddington,and Einstein.There grew around the second law a nearly inpenetrable mystique which only now is being pierced. The second law has no general theoretical proof and,like all physical laws,its status is tied ultimately to experiment.Although many theoretical challenges to it have been advanced and several corroborative experiments have been conducted

Preface The advance of scientific thought in ways resembles biological and geologic transformation: long periods of gradual change punctuated by episodes of radical upheaval. Twentieth century physics witnessed at least three major shifts — relativity, quantum mechanics and chaos theory — as well many lesser ones. Now, early in the 21st, another shift appears imminent, this one involving the second law of thermodynamics. Over the last 20 years the absolute status of the second law has come under increased scrutiny, more than during any other period its 180-year history. Since the early 1980’s, roughly 50 papers representing over 20 challenges have appeared in the refereed scientific literature. In July 2002, the first conference on its status was convened at the University of San Diego, attended by 120 researchers from 25 countries (QLSL2002) [1]. In 2003, the second edition of Leff’s and Rex’s classic anthology on Maxwell demons appeared [2], further raising interest in this emerging field. In 2004, the mainstream scientific journal Entropy published a special edition devoted to second law challenges [3]. And, in July 2004, an echo of QLSL2002 was held in Prague, Czech Republic [4]. Modern second law challenges began in the early 1980’s with the theoretical proposals of Gordon and Denur. Starting in the mid-1990’s, several proposals for experimentally testable challenges were advanced by Sheehan, et al. By the late 1990’s and early 2000’s, a rapid succession of theoretical quantum mechanical challenges were being advanced by C´ˇapek, et al., Allahverdyan, Nieuwenhuizen, et al., classical challenges by Liboff, Crosignani and Di Porto, as well as more experimentally-based proposals by Nikulov, Keefe, Trupp, Gr¨aff, and others. The breadth and depth of recent challenges are remarkable. They span three orders of magnitude in temperature, twelve orders of magnitude in size; they are manifest in condensed matter, plasma, gravitational, chemical, and biological physics; they cross classical and quantum mechanical boundaries. Several have strong corroborative experimental support and laboratory tests attempting bona fide violation are on the horizon. Considered en masse, the second law’s absolute status can no longer be taken for granted, nor can challenges to it be casually dismissed. This monograph is the first to examine modern challenges to the second law. For more than a century this field has lain fallow and beyond the pale of legitimate scientific inquiry due both to a dearth of scientific results and to a surfeit of peer pressure against such inquiry. It is remarkable that 20th century physics, which embraced several radical paradigm shifts, was unwilling to wrestle with this remnant of 19th century physics, whose foundations were admittedly suspect and largely unmodified by the discoveries of the succeeding century. This failure is due in part to the many strong imprimaturs placed on it by prominent scientists like Planck, Eddington, and Einstein. There grew around the second law a nearly inpenetrable mystique which only now is being pierced. The second law has no general theoretical proof and, like all physical laws, its status is tied ultimately to experiment. Although many theoretical challenges to it have been advanced and several corroborative experiments have been conducted

xiv Challenges to the Second Law no experimental violation has been claimed and confirmed.In this volume we will attempt to remain clear on this point;that is,while the second law might be potentially violable,it has not been violated in practice.This being the case,it is our position that the second law should be considered absolute unless experiment demonstrates otherwise.It is also our position,however,given the strong evidence for its potential violability,that inquiry into its status should not be stifled by certain unscientific attitudes and practices that have operated thus far. This volume should be of interest to researchers in any field to which the sec- ond law pertains,especially to physicists,chemists and engineers involved with thermodynamics and statistical physics.Individual chapters should be valuable to more select readers.Chapters 1-2,which give an overview of entropy,the sec- ond law,early challenges,and classical arguments for second law inviolability, should interest historians and philosophers of science.Chapter 3,which devel- ops quantum mechanical formalism,should interest theorists in quantum statisti- cal mechanics,decoherence,and entanglement.Chapters 4-9 unpack individual, experimentally-testable challenges and can be profitably read by researchers in the various subfields in which they arise,e.g.,solid state,plasma,superconductivity, biochemistry.The final chapter explores two topics at the forefront of second law research:thermosynthetic life and physical eschatology.The former is a proposed third branch of life-beyond the traditional two(chemosynthetic and photosyn- thetic)-and is relevant to evolutionary and extremophile biology,biochemistry, and origin-of-life studies.The latter topic explores the fate of life in the cosmos in light of the second law and its possible violation.Roughly 80%of this volume covers research currently in the literature,rearranged and interpreted;the remain- ing 20%represents new,unpublished work.Chapter 3 was written exclusively by Capek (with editing by d.p.s.),Chapters 4-10 exclusively by Sheehan,Chapter 1 primarily by Sheehan,and Chapter 2 jointly.As much as possible,each chapter is self-contained and understandable without significant reference to other chapters. Whenever possible,the mathematical notation is identical to that employed in the original research. It is likely that many of the challenges in this book will fall short of their marks, but such is the nature of exploratory research,particularly when the quarry is as formidable as the second law.It has 180 years of historical inertia behind it and the adamantine support of the scientific community.It has been confirmed by countless experiments and has survived scores of challenges unscathed.Arguably, it is the best tested,most central and profound physical principle crosscutting the sciences,engineering,and humanities.For good reasons,its absolute status is unquestioned. However,as the second law itself teaches:Things change. Daniel P.Sheehan San Diego,California August 4,2004

xiv Challenges to the Second Law no experimental violation has been claimed and confirmed. In this volume we will attempt to remain clear on this point; that is, while the second law might be potentially violable, it has not been violated in practice. This being the case, it is our position that the second law should be considered absolute unless experiment demonstrates otherwise. It is also our position, however, given the strong evidence for its potential violability, that inquiry into its status should not be stifled by certain unscientific attitudes and practices that have operated thus far. This volume should be of interest to researchers in any field to which the sec￾ond law pertains, especially to physicists, chemists and engineers involved with thermodynamics and statistical physics. Individual chapters should be valuable to more select readers. Chapters 1-2, which give an overview of entropy, the sec￾ond law, early challenges, and classical arguments for second law inviolability, should interest historians and philosophers of science. Chapter 3, which devel￾ops quantum mechanical formalism, should interest theorists in quantum statisti￾cal mechanics, decoherence, and entanglement. Chapters 4-9 unpack individual, experimentally-testable challenges and can be profitably read by researchers in the various subfields in which they arise, e.g., solid state, plasma, superconductivity, biochemistry. The final chapter explores two topics at the forefront of second law research: thermosynthetic life and physical eschatology. The former is a proposed third branch of life — beyond the traditional two (chemosynthetic and photosyn￾thetic) — and is relevant to evolutionary and extremophile biology, biochemistry, and origin-of-life studies. The latter topic explores the fate of life in the cosmos in light of the second law and its possible violation. Roughly 80% of this volume covers research currently in the literature, rearranged and interpreted; the remain￾ing 20% represents new, unpublished work. Chapter 3 was written exclusively by ˇ primarily by Sheehan, and Chapter 2 jointly. As much as possible, each chapter is self-contained and understandable without significant reference to other chapters. Whenever possible, the mathematical notation is identical to that employed in the original research. It is likely that many of the challenges in this book will fall short of their marks, but such is the nature of exploratory research, particularly when the quarry is as formidable as the second law. It has 180 years of historical inertia behind it and the adamantine support of the scientific community. It has been confirmed by countless experiments and has survived scores of challenges unscathed. Arguably, it is the best tested, most central and profound physical principle crosscutting the sciences, engineering, and humanities. For good reasons, its absolute status is unquestioned. However, as the second law itself teaches: Things change. Daniel P. Sheehan San Diego, California August 4, 2004 C´apek (with editing by d.p.s.), Chapters 4-10 exclusively by Sheehan, Chapter 1