Preface XV References [1]Sheehan,D.P,Editor,First International Conference on Quantum Limits to the Second Law,AIP Conference Proceedings,Volume 643 (AIP Press,Melville,NY,2002). [2]Leff,H.S.and Rex,A.F.,Marwell's Demon 2:Entropy,Classical and Quantum Information,Computing (Institute of Physics,Bristol, 2003). [3]Special Edition:Quantum Limits to the Second Law of Thermody- namics;Nikulov,A.V.and Sheehan,D.P.,Guest Editors,Entropy 6 1-232(2004). [4 Frontiers of Quantum and Mesoscopic Thermodynamics,Satellite conference of 20th CMD/EPS,Prague,Czech Republic,July 26-29, 2004
Preface xv References [1] Sheehan, D.P., Editor, First International Conference on Quantum Limits to the Second Law, AIP Conference Proceedings, Volume 643 (AIP Press, Melville, NY, 2002). [2] Leff, H.S. and Rex, A.F., Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing (Institute of Physics, Bristol, 2003). [3] Special Edition: Quantum Limits to the Second Law of Thermodynamics; Nikulov, A.V. and Sheehan, D.P., Guest Editors, Entropy 6 1-232 (2004). [4] Frontiers of Quantum and Mesoscopic Thermodynamics, Satellite conference of 20th CMD/EPS, Prague, Czech Republic, July 26-29, 2004
xvi Challenges to the Second Law Acknowledgements It is a pleasure to acknowledge a number of colleagues,associates,and staff who assisted in the completion of this book.We gratefully thank Emily Perttu for her splendid artwork and Amy Besnoy for her library research support.The following colleagues are acknowledged for their review of sections of the book,particularly as they pertain to their work:Lyndsay Gordon,Jack Denur,Peter Keefe,Armen Allahverdyan,Theo Nieuwenhuizen,Andreas Trupp,Bruno Crosignani,Jeremy Fields,Anne Sturz,Vaclav Spicka,and William Sheehan.Thank you all! Special thanks are extended to USD Provost Frank Lazarus,USD President- Emeritus Alice B.Hayes,and Dean Patrick Drinan for their financial support of much of the research at USD.This work was also tangentially supported by the Research Corporation and by the United States Department of Energy. We are especially indebted to Alwyn van der Merwe for his encouragement and support of this project.We are also grateful to Sabine Freisem and Kirsten Theunissen for their patience and resolve in seeing this volume to completion.I (d.p.s.)especially thank my father,William F.Sheehan,for introducing me to this ancient problem. Lastly,we thank our lovely and abiding wives,Jana and Annie,who stood by us in darkness and in light. D.P.S. (V.C) Postscript Although this book is dedicated to our wives,for me (d.p.s.),it is also dedicated to Vlada,who died bravely October 28,2002.He was a lion of a man,possessing sharp wit,keen insight,indominable spirit,and deep humanity.He gave his last measure of strength to complete his contribution to this book,just months before he died.He is sorely missed. d.p.s. Juy,2004
xvi Challenges to the Second Law Acknowledgements It is a pleasure to acknowledge a number of colleagues, associates, and staff who assisted in the completion of this book. We gratefully thank Emily Perttu for her splendid artwork and Amy Besnoy for her library research support. The following colleagues are acknowledged for their review of sections of the book, particularly as they pertain to their work: Lyndsay Gordon, Jack Denur, Peter Keefe, Armen Allahverdyan, Theo Nieuwenhuizen, Andreas Trupp, Bruno Crosignani, Jeremy Fields, Anne Sturz, V´aclav Spiˇ ˇ cka, and William Sheehan. Thank you all! Special thanks are extended to USD Provost Frank Lazarus, USD PresidentEmeritus Alice B. Hayes, and Dean Patrick Drinan for their financial support of much of the research at USD. This work was also tangentially supported by the Research Corporation and by the United States Department of Energy. We are especially indebted to Alwyn van der Merwe for his encouragement and support of this project. We are also grateful to Sabine Freisem and Kirsten Theunissen for their patience and resolve in seeing this volume to completion. I (d.p.s.) especially thank my father, William F. Sheehan, for introducing me to this ancient problem. Lastly, we thank our lovely and abiding wives, Jana and Annie, who stood by us in darkness and in light. D.P.S. (V.C.) ˇ Postscript Although this book is dedicated to our wives, for me (d.p.s.), it is also dedicated to Vl´ada, who died bravely October 28, 2002. He was a lion of a man, possessing sharp wit, keen insight, indominable spirit, and deep humanity. He gave his last measure of strength to complete his contribution to this book, just months before he died. He is sorely missed. d.p.s. July, 2004
1 Entropy and the Second Law Various formulations of the second law and entropy are reviewed.Longstand- ing foundational issues concerned with their definition,physical applicability and meaning are discussed. 1.1 Early Thermodynamics The origins of thermodynamic thought are lost in the furnace of time.However, they are written into flesh and bone.To some degree,all creatures have an innate 'understanding'of thermodynamics-as well they should since they are bound by it.Organisms that display thermotaxis,for example,have a somatic familiarity with thermometry:zeroth law.Trees grow tall to dominate solar energy reserves: first law.Animals move with a high degree of energy efficiency because it is understood'at an evolutionary level that energy wasted cannot be recovered: second law.Nature culls the inefficient. Human history and civilization have been indelibly shaped by thermodynamics. Survival and success depended on such things as choosing the warmest cave for winter and the coolest for summer,tailoring the most thermally insulating furs, rationing food,greasing wheels against friction,finding a southern exposure for a home(in the northern hemisphere),tidying up occasionally to resist the tendencies of entropy.Human existence and civilization have always depended implicitly on
1 Entropy and the Second Law Various formulations of the second law and entropy are reviewed. Longstanding foundational issues concerned with their definition, physical applicability and meaning are discussed. 1.1 Early Thermodynamics The origins of thermodynamic thought are lost in the furnace of time. However, they are written into flesh and bone. To some degree, all creatures have an innate ‘understanding’ of thermodynamics — as well they should since they are bound by it. Organisms that display thermotaxis, for example, have a somatic familiarity with thermometry: zeroth law. Trees grow tall to dominate solar energy reserves: first law. Animals move with a high degree of energy efficiency because it is ‘understood’ at an evolutionary level that energy wasted cannot be recovered: second law. Nature culls the inefficient. Human history and civilization have been indelibly shaped by thermodynamics. Survival and success depended on such things as choosing the warmest cave for winter and the coolest for summer, tailoring the most thermally insulating furs, rationing food, greasing wheels against friction, finding a southern exposure for a home (in the northern hemisphere), tidying up occasionally to resist the tendencies of entropy. Human existence and civilization have always depended implicitly on
2 Challenges to the Second Law an understanding of thermodynamics,but it has only been in the last 150 years that this understanding has been codified.Even today it is not complete. Were one to be definite,the first modern strides in thermodynamics began perhaps with James Watt's (1736-1819)steam engine,which gave impetus to what we now know as the Carnot cycle.In 1824 Sadi Nicolas Carnot (1796-1832), published his only scientific work,a treatise on the theory of heat (Reflerions sur la Puissance Motice du Feu)[1].At the time,it was not realized that a portion of the heat used to drive steam engines was converted into work.This contributed to the initial disinterest in Carnot's research. Carnot turned his attention to the connection between heat and work,abandon- ing his previous opinion about heat as a fluidum,and almost surmised correctly the mechanical equivalent of heat.In 1846,James Prescott Joule (1818-1889) published a paper on thermal and chemical effects of the electric current and in another (1849)he reported mechanical equivalent of heat,thus erasing the sharp boundary between mechanical and thermal energies.There were also others who, independently of Joule,contributed to this change of thinking,notably Hermann von Helmholtz (1821-1894). Much of the groundwork for these discoveries was laid by Benjamin Thompson (Count of Rumford 1753-1814).In 1798,he took part in boring artillery gun barrels.Having ordered the use of blunt borers-driven by draught horses-he noticed that substantial heat was evolved,in fact,in quantities sufficient to boil appreciable quantities of water.At roughly the same time,Sir Humphry Davy (1778-1829)observed that heat developed upon rubbing two pieces of metal or ice,even under vacuum conditions.These observations strongly contradicted the older fluid theories of heat. The law of energy conservation as we now know it in thermodynamics is usually ascribed to Julius Robert von Mayer(1814-1878).In classical mechanics,however, this law was known intuitively at least as far back as Galileo Galilei (1564-1642). In fact,about a dozen scientists could legitimately lay claim to discovering energy conservation.Fuller accounts can be found in books by Brush [2]and von Baeyer [3].The early belief in energy conservation was so strong that,since 1775,the French Academy has forbidden consideration of any process or apparatus that purports to produce energy ex nihilo:a perpetuum mobile of the first kind. With acceptance of energy conservation,one arrives at the first law of ther- modynamics.Rudolph Clausius (1822-1888)summarized it in 1850 thus:"In any process,energy may be changed from one to another form (including heat and work),but can never be produced or annihilated."With this law,any possibility of realizing a perpetuum mobile of the first kind becomes illusory. Clausius'formulation still stands in good stead over 150 years later,despite unanticipated discoveries of new forms of energy-e.g.,nuclear energy,rest mass energy,vacuum energy,dark energy.Because the definition of energy is malleable, in a practical sense,the first law probably need not ever be violated because,were one to propose a violation,energy could be redefined so as to correct it.Thus, conservation of energy is reduced to a tautology and the first law to a powerfully convenient accounting tool for the two general forms of energy:heat and work. Unfortunately,this tract was not published,but was found in his inheritance in 1878
2 Challenges to the Second Law an understanding of thermodynamics, but it has only been in the last 150 years that this understanding has been codified. Even today it is not complete. Were one to be definite, the first modern strides in thermodynamics began perhaps with James Watt’s (1736-1819) steam engine, which gave impetus to what we now know as the Carnot cycle. In 1824 Sadi Nicolas Carnot (1796-1832), published his only scientific work, a treatise on the theory of heat (R´eflexions sur la Puissance Motice du Feu) [1]. At the time, it was not realized that a portion of the heat used to drive steam engines was converted into work. This contributed to the initial disinterest in Carnot’s research. Carnot turned his attention to the connection between heat and work, abandoning his previous opinion about heat as a fluidum, and almost surmised correctly the mechanical equivalent of heat1. In 1846, James Prescott Joule (1818-1889) published a paper on thermal and chemical effects of the electric current and in another (1849) he reported mechanical equivalent of heat, thus erasing the sharp boundary between mechanical and thermal energies. There were also others who, independently of Joule, contributed to this change of thinking, notably Hermann von Helmholtz (1821-1894). Much of the groundwork for these discoveries was laid by Benjamin Thompson (Count of Rumford 1753-1814). In 1798, he took part in boring artillery gun barrels. Having ordered the use of blunt borers – driven by draught horses – he noticed that substantial heat was evolved, in fact, in quantities sufficient to boil appreciable quantities of water. At roughly the same time, Sir Humphry Davy (1778-1829) observed that heat developed upon rubbing two pieces of metal or ice, even under vacuum conditions. These observations strongly contradicted the older fluid theories of heat. The law of energy conservation as we now know it in thermodynamics is usually ascribed to Julius Robert von Mayer (1814-1878). In classical mechanics, however, this law was known intuitively at least as far back as Galileo Galilei (1564-1642). In fact, about a dozen scientists could legitimately lay claim to discovering energy conservation. Fuller accounts can be found in books by Brush [2] and von Baeyer [3]. The early belief in energy conservation was so strong that, since 1775, the French Academy has forbidden consideration of any process or apparatus that purports to produce energy ex nihilo: a perpetuum mobile of the first kind. With acceptance of energy conservation, one arrives at the first law of thermodynamics. Rudolph Clausius (1822-1888) summarized it in 1850 thus: “In any process, energy may be changed from one to another form (including heat and work), but can never be produced or annihilated.” With this law, any possibility of realizing a perpetuum mobile of the first kind becomes illusory. Clausius’ formulation still stands in good stead over 150 years later, despite unanticipated discoveries of new forms of energy — e.g., nuclear energy, rest mass energy, vacuum energy, dark energy. Because the definition of energy is malleable, in a practical sense, the first law probably need not ever be violated because, were one to propose a violation, energy could be redefined so as to correct it. Thus, conservation of energy is reduced to a tautology and the first law to a powerfully convenient accounting tool for the two general forms of energy: heat and work. 1Unfortunately, this tract was not published, but was found in his inheritance in 1878
Chapter 1:Entropy and the Second Law 3 In equilibrium thermodynamics,the first law is written in terms of an additive state function,the internal energy U,whose exact differential dU fulfills dU =6Q+6W. (1.1) Here 6Q and ow are the inexact differentials of heat and work added to the system.(In nonequilibrium thermodynamics,there are problems with introducing these quantities rigorously.)As inexact differentials,the integrals of 60 and oW are path dependent,while dU,an exact differential is path independent;thus, U is a state function.Other state functions include enthalpy,Gibbs free energy, Helmholtz free energy and,of course,entropy. 1.2 The Second Law:Twenty-One Formulations The second law of thermodynamics was first enunciated by Clausius(1850)[4] and Kelvin (1851)[5],largely based on the work of Carnot 25 years earlier [1]. Once established,it settled in and multiplied wantonly;the second law has more common formulations than any other physical law.Most make use of one or more of the following terms-entropy,heat,work,temperature,equilibrium,perpetuum mobile-but none employs all,and some employ none.Not all formulations are equivalent,such that to satisfy one is not necessarily to satisfy another.Some versions overlap,while others appear to be entirely distinct laws.Perhaps this is what inspired Truesdell to write,"Every physicist knows exactly what the first and second laws mean,but it is my experience that no two physicists agree on them.” Despite-or perhaps because of-its fundamental importance,no single formulation has risen to dominance.This is a reflection of its many facets and applications,its protean nature,its colorful and confused history,but also its many unresolved foundational issues.There are several fine accounts of its his- tory [2,3,6,7;here we will give only a sketch to bridge the many versions we introduce.Formulations can be catagorized roughly into five catagories,depend- ing on whether they involve:1)device and process impossibilities;2)engines;3) equilibrium;4)entropy;or 5)mathematical sets and spaces.We will now consider twenty-one standard (and non-standard)formulations of the second law.This sur- vey is by no means exhaustive. The first explicit and most widely cited form is due to Kelvin2 [5,8. (1)Kelvin-Planck No device,operating in a cycle,can produce the sole effect of extraction a quantity of heat from a heat reservoir and the performance of an equal quantity of work. 2William Thomson (1824-1907)was known from 1866-92 as Sir William Thomson and after 1892 as Lord Kelvin of Largs
Chapter 1: Entropy and the Second Law 3 In equilibrium thermodynamics, the first law is written in terms of an additive state function, the internal energy U, whose exact differential dU fulfills dU = δQ + δW. (1.1) Here δQ and δW are the inexact differentials of heat and work added to the system. (In nonequilibrium thermodynamics, there are problems with introducing these quantities rigorously.) As inexact differentials, the integrals of δQ and δW are path dependent, while dU, an exact differential is path independent; thus, U is a state function. Other state functions include enthalpy, Gibbs free energy, Helmholtz free energy and, of course, entropy. 1.2 The Second Law: Twenty-One Formulations The second law of thermodynamics was first enunciated by Clausius (1850) [4] and Kelvin (1851) [5], largely based on the work of Carnot 25 years earlier [1]. Once established, it settled in and multiplied wantonly; the second law has more common formulations than any other physical law. Most make use of one or more of the following terms — entropy, heat, work, temperature, equilibrium, perpetuum mobile — but none employs all, and some employ none. Not all formulations are equivalent, such that to satisfy one is not necessarily to satisfy another. Some versions overlap, while others appear to be entirely distinct laws. Perhaps this is what inspired Truesdell to write, “Every physicist knows exactly what the first and second laws mean, but it is my experience that no two physicists agree on them.” Despite — or perhaps because of — its fundamental importance, no single formulation has risen to dominance. This is a reflection of its many facets and applications, its protean nature, its colorful and confused history, but also its many unresolved foundational issues. There are several fine accounts of its history [2, 3, 6, 7]; here we will give only a sketch to bridge the many versions we introduce. Formulations can be catagorized roughly into five catagories, depending on whether they involve: 1) device and process impossibilities; 2) engines; 3) equilibrium; 4) entropy; or 5) mathematical sets and spaces. We will now consider twenty-one standard (and non-standard) formulations of the second law. This survey is by no means exhaustive. The first explicit and most widely cited form is due to Kelvin2 [5, 8]. (1) Kelvin-Planck No device, operating in a cycle, can produce the sole effect of extraction a quantity of heat from a heat reservoir and the performance of an equal quantity of work. 2William Thomson (1824-1907) was known from 1866-92 as Sir William Thomson and after 1892 as Lord Kelvin of Largs