Challenges to the Second Law of Thermodynamics 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 ápek Charles University, Prague, Czech Republic and Daniel P Sheehan University of San Diego, San Diego, California, U.S.A A C.I.P Catalogue record for this book is available from the Library of Congress ISBN 1-4020-3015-0 (HB) ISBN 1-4020-3016-9 (e-book) Published by Springer, P.O Box 17, 3300 AA Dordrecht, The Netherlands Sold and distributed in North, Central and South America by Springer, 101 Philip Drive, Norwell, MA 02061, U.S.A In all other countries, sold and distributed by Springer, P.O Box 322, 3300 AH Dordrecht, The Netherlands Printed on acid-free paper All Rights Reserved © 2005 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work Printed in the Netherlands To our wives, Jana and Annie In Memoriam Vl´da a (1943-2002) Contents Preface Acknowledgements xiii xvi Entropy and the Second Law 1.1 Early Thermodynamics 1.2 The Second Law: Twenty-One Formulations 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 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 Modern Quantum Challenges: Theory 3.1 Prolegomenon 53 Challenges to the Second Law 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 3.6.2 3.6.3 3.6.4 3.6.5 3.6.6 3.6.7 3.6.8 Fish-Trap Model 76 Semi-Classical Fish-Trap Model 83 Periodic Fish-Trap Model 87 Sewing Machine Model 91 Single Phonon Mode Model 97 Phonon Continuum Model 101 Exciton Diffusion Model 101 Plasma Heat Pump Model 102 3.7 Disputed Quantum Models 105 3.7.1 Porto Model 106 3.7.2 Novotn´ 106 y 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 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 Contents ix 4.5 Bose-Einstein Condensation and the Second Law 134 4.6 Quantum Coherence and Entanglement 135 4.6.1 4.6.2 4.6.3 4.6.4 Introduction Spin-Boson Model Mesoscopic LC Circuit Model Experimental Outlook References 135 136 137 139 141 Modern Classical Challenges 5.1 Introduction 145 5.2 Gordon Membrane Models 146 5.2.1 5.2.2 5.2.3 5.2.4 5.2.5 Introduction Membrane Engine Molecular Trapdoor Model Molecular Rotor Model Discussion 146 147 150 152 154 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 Gravitational Challenges 6.1 Introduction 175 6.2 Asymmetric Gravitator Model 177 6.2.1 6.2.2 6.2.3 6.2.4 Introduction 177 Model Specifications 178 One-Dimensional Analysis 180 Numerical Simulations 183 Chapter 10: Special Topics 333 [43] Eddington, A.S., Nature 127 447 (1931) [44] Gold, T., Am J Phys 30 403 (1962) [45] de Chardin, T., The Phenomenon of Man, translated by Wall, B., (Collins, London, 1959) [46] Barrow, J.D., and Tipler, F.J., Nature 276 453 (1978) [47] Kutrov´tz, G., Open Syst Inf Dyn 349 (2001) a [48] Popper, K.R., The Poverty of Historicism (Routledge and Kegan Paul, London, 1957; originally published in Economica, 1944/45) [49] Popper, K.R., Brit J Philos Sci 117 (1950) [50] Shakespeare, W., Hamlet (ca 1600) [51] von Helmholtz, H., On the Interaction of the Natural Forces (1854), in Popular Scientific Lectures, Kline, M., Editor (Dover, New York, 1961) [52] Clausius, R., Ann Phys (Leipziz) 125 353 (1865) [53] Clausius, R., Philos Mag 35 405 (1868) [54] Russell, B., Why I Am Not a Christian (Allen and Unwin, New York, 1957) pg 107 [55] Bernal, J.D., The World, the Flesh, and the Devil, 2nd Ed (Indiana University Press, Bloomington, 1969, 1st Ed 1929) pg 28 [56] Atkins, P., in The Nature of Time, Flood, R and Lockwood, M., Eds (Basil Blackwell, Oxford, 1986) pg 98 [57] Dodelson, S., Modern Cosmology (Academic Press, Amsterdam, 2003) [58] Rees, M.J., Observatory 89 193 (1969) [59] Bludman, S.A., Nature 308 319 (1984) [60] Ford, L.H., Gen Relativ Gravit 19 325 (1987) [61] Krauss, L.M and Turner, M.S., Gen Relativ Gravit 31 1453 (1999) [62] Frautschi, S., Science 217 593 (1982) [63] Bekenstein, J.D., Phys Rev D 23 287 (1981) [64] Bekenstein, J.D., Phys Rev D 2333 (1973) [65] Hawking, S.W., Nature 274 30 (1974) 334 Challenges to the Second Law [66] Hawking, S.W Commun Math Phys 43 199 (1975) [67] Sheehan, D.P., unpublished (1995) [68] Hoyle, F., The Black Cloud, (Harper, New York, 1957) ˇ [69] Capek, K., R.U.R trans Selver, P (Doubleday, Garden City, N.Y., 1923) [70] Wheeler, J.A., IBM J Res Develop 32 (1988) [71] Rauen, K., Infin Energy 10/55 29 (2004) [72] Einstein, A ‘Autobiographical Notes’, in Schilpp, P.A., Editor, Albert Einstein: Philosopher-Scientist, Vol (Cambridge University Press, Cambridge, 1970) [73] Eddington, A., The Nature of the Physical World (Everyman’s Library, J.M Dent, London) [74] Fermi, E Thermodynamics (Dover Publications, New York, 1936) [75] Clausius, R., Phil Mag 4, 12 (1856) [76] Maxwell, J.C., in Life of John William Strutt, Third Baron Rayleigh, Strutt, R.J., Editor (E Arnold, London, 1924) pp 47-48 [77] Cengel, Y.A and Boles, M.A., Thermodynamics: An Engineering ¸ Approach, 2nd Ed (McGraw-Hill, New York, 1994) [78] Horgan, J., The End of Science (Broadway Books, New York, 1996) [79] Maddox, J What Remains to be Discovered (The Free Press, New York, 1998) [80] Park, R.L., Voodoo Science (Oxford University Press, Oxford, 2000) [81] Maddox, J., Nature 412, 903 (2002) [82] Lieb, E.H and Yngvason, J., Phys Today 53, 32 (2000) [83] Brillouin, L., Amer Sci 37, 554 (1949) [84] Zolina, P., Heat Death of the Universe and Other Stories (McPherson, Kingston, NY, 1988) [85] Gordon, G (Lord Byron) in Poetry, An Introduction, Lane, W.G (D.C Heath and Co., 1968); Frost, R., ibid.; Macleish, A., ibid 335 Plate I Phase space diagram vx versus r for standard gravitator (3000 patch crossings; 30o polar domes over S1 and S2); (rpatch = 2.475 × 106 m) 336 Challenges to the Second Law Plate II Phase space diagram vr versus r for standard gravitator (3000 patch crossings; 30o polar domes over S1 and S2; rG < rpatch < rc ) 337 Plate III Phase space diagram vr versus T for standard gravitator (3000 patch crossings, 30o polar domes over S1 and S2, rpatch = 2.405 × 106 m) 338 Challenges to the Second Law Plate IV Atlas 2-D numerical simulations of electric field for three related variations of the standard device a) Case 1: standard device without J-II gap; b) Case 2: standard device; c) Case 3: standard device with 300˚ x 600˚ undoped silicon A A piston at gap center 339 Plate V Sequence of 2-D Atlas simulations of electric field for standard device with static piston at various locations in J-II channel 340 Challenges to the Second Law Plate VI Device power and power density over range of devices size-scaled to standard device (TOP): Maximum power output versus gap width (xg ) and contact fraction (fc ) Contours vary linearly from 10−9 W/device (red) to 1.2 × 10−8 W/device (yellow) (BOTTOM): Power density (Wm−3 ) versus xg and fc Contours vary logarithmically from 101 Wm−3 (red) to 1010 Wm−3 (yellow) Star indicates location of standard device 341 10 10 10 10 Force [N] 10 10 10 10 10 -2 10 µm -3 30 µm -4 -5 90 µm -6 -7 -0 -8 10 -9 10 -10 Vo=0.6V 10 -1 -2 -3 10 10 -11 10 electrostatic cantilever spring van der Waals -12 -10 10 -4 10 -9 10 -8 10 Dynamic Separation yg - y[m] -7 10 -6 10 Plate VII Force (N) on hammer versus dynamic separation (m) with anvil (SUMMiTT M case) Spring force (green); van der Waals force (blue); Electrostatic force (red) Device parameters: lz = lh = 5µm, tc = 4.5µm, th = 6µm, lc = 10, 30, 90µm; 10−4 ≤ η ≤ 1, Vo = Vbi = 0.6V 342 Challenges to the Second Law 90 10 80 0.6 70 10 1.0 60 Q 50 2.0 40 10 90 80 10 30 70 5.0 60 50 20 40 -1 10 30 20 10 10 10 10 τe / τm Plate VIII Minimum external bias voltage required for sustained oscillation for τe SUMMiTT M device (Figure 9.13b), plotted versus Q and τm In sweet spot (0.25 ≤ τe τm ≤ 4) and (2×10 ≤ Q ≤ 10 ), low dc-voltage (1V ≤ V ≤ 5V) drives oscillation Index A additivity (entropy), 14, 19 adiabatic accessibility, 10, 19 adiabatic piston, 159 adsorption/desorption (gas), 215 algorithmic randomness, 21 Allahverdyan, A.E., 69, 135 A-N Theorem, 69 spin-boson model, 136 mesoscopic LC circuit model, 137 Archaea, 310 Argyres-Kelly projector, 58 asymmetric momentum fluxes, 308 ATP, 313, 316 B BBGKY hierarchy, 45 Bekenstein limit, 324 biomembrane, 146, 312 Boltzman-Gibbs entropy, 15 Boltzmann H-theorem, 43 Bowles, J., 268 Brillouin, L., 39 Brownian motion, 108, 110, 156 C cantilever oscillator, 291 capacitive chemical reactor, 300 ˇa C´pek, V., 76-105 fish-trap (swing), 76 semi-classical fish-trap, 83 periodic fish-trap, 87 sewing machine, 91 single phonon, 97 phonon continuum, 101 exciton diffusion, 101 plasma heat pump, 102 Carath´odory principle, 10, 20 e Carnot, S., chemical nonequilibrium, 211 Clausius, R., 2, 12, 14 CMCE engine (Keefe), 121 coarse grained entropy, 15, 44 coherence length, 118 coherent magnetocaloric effect, 120 coherence, quantum mechancial, 135 correlations, quantum, 67 Crosignani, B., 159 Cruden, B., 262 D Davies, E.B., 64 dc limit (kinetics), 106 density matrix (Gibbsian), 49 Denur, J., 154 Doppler demon, 155 ratchet-pawl engine, 156 detailed balance, 214 Di Porto, P., 159 diode, self-rectifying, 41 Doppler demon, 155 DSPG, 212 Duncan, T., 213 Dyson, F 319 344 E electrocaloric cycle, 164 ensemble, 15 microcanonical, 15 canonical, 16 grand canonical, 16 entanglement (quantum), 135 entropy gradient, 322 entropy production (cosmic), 322 entropy types, 13, 23 algorithmic randomness, 21 Bekenstein-Hawking, 323 Boltzmann-Gibbs, 15 Carath´odory, 20 e Clausius, 14 coarse grained, 15 Dar´czy, 22 o Fisher, 21 generalize, 324 Gyftopolous, 18 Hartley, 23 infinite norm, 23 Lieb-Yngvason, 19 miscellaneous, 23 nonequilibrium, 23 relative, 23 R´nyi, 22 e Shannon, 20 Tsallis, 21 von Neumann, 17 eschatology, 319 exciton diffusion model, 101 extensivity, 19, 176 F FEL, 309 fish-trap (swing) model, 76 quantum, 76 semi-classical, 83 periodic, 87 floating potential (plasma), 243 free energy life (FEL), 309 Challenges to the Second Law Fulton, R., 171 future (far), 319 G gas cycle challenges, 171 gas-surface reactions, 211, 227 generalized master equation (GME), 57, 60 Gordon, L.G.M 146 membrane engine, 147 molecular trapdoor model, 150 molecular rotor model, 152 Gră, R.W., 203 a gravitation, 175 classical paradoxes, 175 Gră experiments, 203 a asymmetric gravitator, 177 Trupp experiments, 206 gravitator (standard), 180 gravito-thermal effect, 202 Gyftopolous, E.P., 7, 18 H-K hammer-anvil model, 291 heat death, coma, 319 inviolability (second law) 42 early classical, 43 modern classical, 44 Jones, R., 262 Keefe, P.D., 121 Kelvin, Lord, kinetic dc limit, 106 Index 345 L N Langevin force, 160 Langmuir probe, 242 Le Chˆtelier’s principle, 217 a LEM, 277 Liboff, R., 169 life, 146, 164, 308 linear electrostatic motor (LEM), 277 Liouville equation, 17 superoperator, 57 Little-Parks effect, 120 Loschmidt, J., 38, 43, 202 demon, 38 gravito-thermal effect, 202 reversibility argument, 43 Nakajima-Zwanzig identity, 58, 108 NEMS, 267 NESS, 25 Nieuwenhuizen, Th.M., 69, 135 A-N theorem, 69 spin-boson model, 136 mesoscopic LC circuit model, 137 Nikulov, A., 125 quantum force, 125 inhomogeneous loop, 127 nonequilibrium, 23, 211 Novotn´ model, 106 y O-P M penetration depth, 118 periodic fish-trap model, 87 macroscopic potential gradient (MPG), perpetuum mobile, 2, 4, 12 Pertuu, E.K., 294 304 phase space portraits, 187 magnetocaloric effect 119 phonon mode model, 97 maximum entropy principle, single phonon, 97 Maxwell’s demon, 35 continuum, 101 Maxwell demons (types), 35 physical eschatology, 319 Brillouin, 40 Pippard, A.B., 119 Doppler, 155 plasma heat pump model, 102 Loschmidt, 38 plasma potential, 243 Maxwell, 35 Plasma I system, 240 self-rectifying diode, 41 Plasma II system, 251 Smoluchowski, 39 Poincar´ recurrence, 43 e Szilard, 40 Pombo, C., 135 Whiting, 38, 177 Porto model, 106 Maxwell, J.C., 35 pressure gradients (DSPG), 211 membrane (cellular), 146, 313 Putnam, A.R., 267 membrane models (Gordon), 146 mesoscopic LC circuit model, 137 MEMS, 267 molecular rotor model, 152 molecular trapdoor model, 150 Mori identity, 108 MPG, 304 mystique (second law), 327 346 Q-R Q-machine, 244, 253 quantum force, 121, 125 Redfield relaxation superoperator, 63 ratchet-pawl model, 156 Rauen, K., 171 rate equations (chemical), 211, 219 S second law, second law, challenges adiabatic piston, 159 asymmetric gravitator, 177 capacitive chemical reactor, 300 chemical pressure gradient, 211 Doppler demon, 155 electrocaloric cycle, 164 exciton diffusion, 101 fish-trap, 76 linear electrostatic motor, 277 gas cycles, 171 gravito-thermal effect, 202, 206 hammer-anvil, 291 inhomogeneous loop, 125 lin electrost motor (LEM), 277 MCME engine, 121 membrane engine, 147 mesoscopic LC circuit, 137 molecular trapdoor, 150 molecular rotor, 152 periodic fish-trap, 87 phonon continuum, 101 plasma I, 240 plasma II, 251 plasma heat pump, 102 ratchet-pawl engine, 156 semi-classical fish-trap, 83 sewing machine, 91 single phonon, 97 spin-boson model, 136 tri-channel, 169 Challenges to the Second Law second law formulations, Carath´odory, 10 e Carnot theorem, Clausius-entropy, Clausius-Heat, efficiency, equilibrium, folksy, 11 generalized, 324 Gibbs, Gyftopolous, heat engines, irreversibility, Kelvin-Planck, Lieb-Ygnvason, 20 Macdonald, perpetual motion, Planck, refrigerators, Thomson-equilibrium, 11 second law inviolability, 42 early, 43 modern, 44 Loschmidt, 43 Zermelo, 43 semi-classical fish-trap model, 83 semiconductor, 268 sewing machine model, 91 Shannon entropy, 20 Sheehan, D.P chemical DSPG, 211 gravitator, 177 hammer-anvil, 291 linear electrostatic motor, 277 plasma I, 240 plasma II, 251 Shibata - -Shingu (SHTS) identity, 59 Smoluchowski, M., 39 spin-boson model, 136 standard gravitator, 180 Strain 121, 310 superconductivity, 117 super-extensivity, 176 superoperator, 59 Szilard engine, 40 Index T thermal capacitor, 268 thermal life, 326 thermodynamics early, first law of, third law of, 28 zeroth law of, 28 thermodynamic limit, 15, 55 thermophile, 310 thermosynthetic life (TL), 308 third law of thermodynamics, 28 time-convolution GME TC-GME, 60, 107 TCL-GME, 60, 110 TL, 308 Tokuyama-Mori identity, 110 tri-channel model, 169 Trupp, A., 164, 206 Tsallis entropy, 21 U-Z van Hove limit, 64 velocity distribution (gravitator), 184 von Mayer, J.R., von Neumann entropy, 17 weak coupling, 55, 64 Wheeler, J.C., 171, 197 Whiting, H., 38, 177 Wright, J.H., 267 Zermelo (Poincar´) recurrence, 43 e zeroth law of thermodynamics, 28 Zhang-Zhang flows, 307 Zhang-Zhang theorem, 307 347 ... Zeroth and Third Laws of Thermodynamics The first law is the skeleton of thermodynamics; the second law is its flesh The first gives structure; the second gives life By comparison, the zeroth and 18... mobile of the second type generally receives the most support Chapter 1: Entropy and the Second Law 13 and the least dissention It is the gold standard of second law formulations If the second law. .. violations of specific formulations of this law in specific situations, as will be shown in Chapter 26 Challenges to the Second Law 1.5 Entropy and the Second Law: Discussion Entropy and the second law