Challenges to The Second Law of Thermodynamics (eBook)

Contents 8
Preface 14
References 16
Acknowledgements 17
1 Entropy and the Second Law 18
1.1 Early Thermodynamics 18
1.2 The Second Law: Twenty-One Formulations 20
1.3 Entropy: Twenty-One Varieties 30
1.4 Nonequilibrium Entropy 40
1.5 Entropy and the Second Law: Discussion 43
1.6 Zeroth and Third Laws of Thermodynamics 44
References 47
2 Challenges (1870-1980) 52
2.1 Maxwell’s Demon and Other Victorian Devils 52
2.2 Exorcising Demons 56
2.3 Inviolability Arguments 59
2.4 Candidate Second Law Challenges 65
References 68
3 Modern Quantum Challenges: Theory 70
3.1 Prolegomenon 70
3.2 Thermodynamic Limit and Weak Coupling 72
3.3 BeyondWeak Coupling: Quantum Correlations 84
3.4 Allahverdyan-Nieuwenhuizen Theorem 86
3.5 Scaling and Beyond 88
3.6 Quantum Kinetic and Non-Kinetic Models 92
3.7 Disputed Quantum Models 122
3.8 Kinetics in the DC Limit 123
3.9 Theoretical Summary 128
References 130
4 Low-Temperature Experiments and Proposals 134
4.1 Introduction 134
4.2 Superconductivity 134
4.3 Keefe CMCE Engine 138
4.4 Nikulov Inhomogeneous Loop 142
4.5 Bose-Einstein Condensation and the Second Law 151
4.6 Quantum Coherence and Entanglement 152
References 158
5 Modern Classical Challenges 162
5.1 Introduction 162
5.2 Gordon Membrane Models 163
5.3 Denur Challenges 171
5.4 Crosignani-Di Porto Adiabatic Piston 176
5.5 Trupp Electrocaloric Cycle 181
5.6 Liboff Tri-Channel 186
5.7 Thermodynamic Gas Cycles 188
References 189
6 Gravitational Challenges 192
6.1 Introduction 192
6.2 Asymmetric Gravitator Model 194
6.3 Loschmidt Gravito-Thermal Effect 219
References 224
7 Chemical Nonequilibrium Steady States 228
7.1 Introduction 228
7.2 Chemical Paradox and Detailed Balance 231
7.3 Pressure Gradients and Reaction Rates 235
7.4 Numerical Simulations 241
7.5 Laboratory Experiments 244
7.6 Discussion and Outlook 250
References 254
8 Plasma Paradoxes 256
8.1 Introduction 256
8.2 Plasma I System 257
8.3 Plasma II System 268
8.4 Jones and Cruden Criticisms 279
References 283
9 MEMS/NEMS Devices 284
9.1 Introduction 284
9.2 Thermal Capacitors 285
9.3 Linear Electrostatic Motor (LEM) 294
9.4 Hammer and Anvil Model 308
9.5 Experimental Prospects 317
References 318
10 Special Topics 320
10.1 Rubrics for Classical Challenges 320
10.2 Thermosynthetic Life 325
10.3 Physical Eschatology 336
10.4 The Second Law Mystique 344
References 348
Color Plates 352
Index 360

2 Challenges (1870-1980) (p.35)

An overview of second law challenges and their resolutions is given for the period 1870-1980, beginning with Maxwell’s demon. Classical second law inviolability proofs are critiqued and from these, candidate regimes are inferred for modern challenges.

2.1 Maxwell’s Demon and Other Victorian Devils
Challenges to the second law began soon after it was discovered. The first, most enduring, and most edifying of these is James Clark Maxwell’s celebrated demon. Here we only sketch the many lives and reported deaths of this clever gedanken heat fairy, since an adequate treatment would fill an entire volume by itself. A superb discussion and anthology is presented by Leff and Rex [1].

Maxwell’s demon was born with a letter from Maxwell to Peter Guthrie Tait in 1867. Maxwell’s intention was "to pick a hole" in the second law by imagining a process whereby molecules could be processed on an individual basis so as to engineer microscopically a temperature gradient. Maxwell writes:

. . . Let him [demon] first observe the molecules in [compartment] A and when he sees one coming the square of whose velocity is less than the mean sq. vel. of the molecules in B let him open the hole and let it go into B. Next let him watch for a molecule of [compartment] B, the square of whose velocity is greater than the mean sq. vel. in A, and when it comes to the hole let him draw the slide and let it go into A, keeping the slide shut for all other molecules...

Maxwell’s original description is both clear and historically important so we quote more extensively from his book [2]. One of the best established facts in thermodynamics is that it is impossible in a system enclosed in an envelope which permits neither change of volume nor passage of heat, and in which both the temperature and the pressure are everywhere the same, to produce any inequality of temperature or of pressure without the expenditure of work.

This is the second law of thermodynamics, and it is undoubtedly true as long as we can deal with bodies only in mass, and have no power of perceiving or handling the separate molecules of which they are made up. But if we conceive a being whose faculties are so sharpened that he can follow every molecule in its course, such a being whose attributes are still as essentially finite as our own, would be able to do what is at present impossible to us.

For we have seen that the molecules in a vesselful of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower ones to pass from B to A.