USD Conference

Quantum Limits to the Second Law Conference
University of San Diego
July 28 -31, 2002

Roy Lisker, for Ferment Magazine
September 9,2002

On July 26th I visited with Paul and Eva Kirsh in Santa Monica. A few months before my coming to California, Paul Kirsh had contacted me by E-Mail with regard to the articles upload in the Ferment Magazine website on the life and works of Alexander Yesenin-Volpin, the famous Russian dissident and logician.(See VOLPIN Paul and his wife, Eva, invited me to stay overnight on July 26th. The next day they drove me to San Diego. We were two hours behind schedule on the morning of Saturday, July 27th, when we drove out of Santa Monica at noon, searching for the entrance to Highway 5.

A trip from Los Angeles to San Diego should not take more than 3 hours. Yet the congestion was such that for much of the trip we were traveling at no more than 20 miles per hour. For most of the trip we rarely went above 40. It was only upon entering the city limits that we were able to race along as far as the campus of San Diego State college. The time was 5:30: we'd spent over 5 hours on the road.

Using the Kirsh's cell phone I placed a call to Lee Conte, friend of a mutual friend, who'd agreed to put me up for the night and take me over to the conference the following morning. He checked out my location on a Yahoo map, and picked me up in less than half an hour.

Lee works as a telecommunications engineer for AT&T. He'd only recently come out to San Diego. Lee had already decided what we should do for the evening. After I'd cleaned up a taken a short nap, he drove us over to the San Diego Zoo. Lee is quite fond of animals and had been to the Zoo several times before. On this occasion he was hoping to catch some of the nocturnal animals coming out of their lairs. Lee asked me questions about Thermodynamics and Mathematics and I interrogated him on the lives of the denizens of the Zoo.

The artificially "natural" settings of the Zoo were impressive as models of construction, landscaping and art, but it didn't seem to me that the animals were terribly happy in them. One must agree that it's very dangerous for an animal to be out alone in the wild, say on the plains or in jungles, but they can't be very happy either, alone in a cage with no other creatures, ( even if they are enemies) , in sight.(See4 Nature Myths) Lee admitted that this problem had worried him also. He felt that, as zoos go, the one in San Diego did what it could to make its residents feel at home, but there was no way it could hope to reproduce the ambience of their natural habitat.

It led me to speculate on the strangeness of our world. Earth appear to be a place wherein creatures remove other creatures from their natural home, place them in contrived settings for their own amusement, then worry about their well-being.

The following morning, Sunday, July 28th, I placed a call with Daniel Sheehan, organizer of the Second Law Conference. The opening plenary address would take place at 7 PM. Starting at 11 I could check into my room in the Alcala Vista housing quad of USD.

After breakfast I amused myself working out an effective registration for playing Bach's Italian Concerto on Lee's large electronic Casio keyboard. My experiments culminated in an equilibrium state of strings in the right hand against trombones in the bass. At 11 Lee drove me over to the UCD campus.

The University of San Diego ( not to be confused with the University of California at San Diego) is co-essential with a very long, linearly extended campus. Therein one may find grandiose buildings and sweeping thoroughfares, with offset gardens, fountains, grassy plots and tropical trees. The whole production sits in a desert, average rainfall 4 inches a year. This being a drought year, there's been no more than an inch of rain.

The cost of maintaining so lavish an establishment must cost many millions of dollars . Given the costs the enrollment is remarkably small: around 5000 undergraduates . In a few words : USD is a private Catholic university endowed by billionaires, for a small student population consisting largely of with football jocks and valley girls. Athletics plays a large role here, as one could see from all the young people wandering around the campus, wearing the uniforms of their clubs, teams and summer institutes. The bookstore in the basement of Loma Hall contains little more than pulp detective fiction, a few best-sellers and textbooks.

(Comment by Daniel Sheehan: " Unfortunately, we're not endowed by billionaires here, merely by thousandaires and perhaps a few millionaires. Also, we do have a few scholars in addition to the jocks and valley girls.)"

Against this backdrop of vigorous health the delegation to QLSL2 appeared both seedy and eminent to a fault . It had been projected that no more than 40 delegates would show up. As it turned out, there were more than 120 of us, from 23 countries: Japan, the Czech Republic, Russia, Italy,Canada, Mexico, Germany, France, the UK, Holland, India, the United States and others. It must have been the great interest in the topics under discussion that brought the delegations , it being rather unlikely that they would have traveled such great distances just for the good eating and refreshing ocean breeze, although there were plenty of both.

Four themes structured the conference. This brief report will concetrate on a few of the lectures in which they were given prominence:

  1. (i) Historical reviews of the development of Thermodynamics from Sadi Carnot to the present day.

  2. (ii) Devising a statement of the Second Law that everyone could agree with.

  3. (iii) Analyses, arguments for and against the celebrated thought experiment known as the "Maxwell Demon"

  4. (iv) Presentations of theoretical and experimental challenges to the Second Law at the quantum level.

Starting from "Law Zero ", there are 4 Laws of Thermodynamics. The Second Law is not only the most controversial among them, it may well be the most controversial "principle" in all of Physics, (classical or modern) ! Perhaps it has as little right to be called a "law" as do proverbs, such as : "Honesty is the best policy", or: "He who hesitates is lost, or: "Don't cry over spilt milk", etc. Much as each of these embody a grain of truth, the same may be said of the Second Law. By the end of the QLSL2 conference I was proposing a "4th Law of Thermodynamics", to wit : The 2nd Law Of Thermodynamics Will Always Be Controversial. "

Summarizing the 4 Laws of Thermodynamics:

  1. Zeroeth Law:If two systems at the same temperature are brought into contact no work will be done. Otherwise stated, two systems in equilibrium at the same temperature will remain in equilibrium if they are brought into contact. The notions of "temperature" and "equilibrium" are closely connected. In the classical theory, temperature can only be defined for systems in equilibrium.

    One can of course argue at length about exactly what is meant by "contact": Proximity ?( How close?) ; Causal connectedness? Quantum Entanglement? Proximity by quantum entanglement was a recurring theme in many of the talks.

  2. First Law: If heat is introduced into a system, the change in energy DE , is equal to the amount of heat DQ introduced minus the amount of mechanical work DW performed: DE = DQ-DW. In essence this states that heat is a form of energy. One can therefore apply the principle of the conservation of energy to it in combination with whatever changes ( in pressure, volume or temperature), that are brought about by its introduction. These visible changes are grouped together under the concept of "work", a term as difficult to pin down in physics as it is in economics.

  3. Second Law: A major theme at this conference was that the 2nd Law has historically been stated in different ways. These are equivalent in most situations, yet not in all. Many of these exceptional situations come from the Quantum Theory, which is why the conference stressed the notion of quantum limits to the 2nd Law.

    Several of these classical statements were critically examined during the conference. It was shown that, not only are there crucial differences between the statements of the 2nd Law, but that traditional connections between the 2nd Law, Entropy, Irreversibility and the Arrow of Time are over-simplifications.

    At the level of daily experience and observation, the 2nd Law can be understood to mean that heat can never pass from a cold object to a warm one; equivalently, that mechanical work can not be extracted against the flow of heat from warm to cold. If, as in a steam engine, one tries to "recycle" the mechanism by alternating a state of steady temperature ( isothermal), with one of steady heat (adiabatic), a certain percentage of the heat will be unrecoverable from the cycle. This is called the Inefficiency. The measure of this inefficiency is called the Entropy.

    Whereas everyone has had direct experience of the phenomenon of Heat, it is not well-defined scientifically unless certain variables are kept constant. Entropy on the other hand, a notion lying somewhere between an abstraction and a catalyst, is a well-defined quantity, if one means by quantity an observable whose states are independent of the way they are attained or measured.

    In fact Classical Thermodynamics uses Entropy to quantify Heat and not the contrary. The basic equation is dS = dQ/T . Here Entropy (S) , and Temperature (T) , are total differentials, which means that their values in a given state ( Pressure, Volume) of a system, are independent of the way that state is reached. Heat (Q) is not a total differential; its value is a function of the amount of work needed to arrive at that state.

    Even the notion of Temperature, however, is somewhat nebulous, in that there are disputes over its proper dimensions or units. One can say, roughly, that although temperature is spoken of as existing at an isolated point, ( say the tip of the thermometer) , the temperature is really a kind of mean energy averaged over the random motions of a huge number of particles, under the assumption of some kind of global homogeneity.

    Succinctly , the 2nd Law turns out to be merely the collection of all the ways in which its been stated.

  4. Third Law : Entropy vanishes at Absolute Zero. This may also be interpreted to mean, using arguments from Quantum Theory, that no system can ever reach Absolute Zero.

Keynote Address 6:30 PM, July 28th, 2002
Joan Kroc Institute for Peace and Justice
Craig Callender, Philosopher of Science
"Who's Afraid of Maxwell's Demon- and Which One?"

The Maxwell Demon is the very paradigm of the Thought Experiment. Among these one finds the Schršdinger Cat , the Einstein>-Podolsky-Rosen experiment, and the fantasy of 'riding a light wave', which is supposed to have inspired Einstein into formulating Relativity. In recapitulating the history of re-interpretations of the Maxwell Demon from its statement in 1866 to the present, Craig Callender was also invoking the usefulness and also the limitations of the Thought Experiment as a tool in theoretical physics.

No other science uses thought experiments as much as theoretical physics: their role in physics may be compared to that of the "Magical If" in Stanislavski's Method for actors . Almost by definition, the situation in a thought experiment cannot be constructed in the real world : it would then be a real experiment. The fact that one cannot construct the situation described by the thought experiment may be itself an important statement about the physical world.

One can look upon thought experiments as realizations of the axioms for the purpose of clarifying the foundations of a subject. However Physics is notoriously resistant to axiomatization. All efforts to give an axiomatic formulation to Mechanics, Thermodynamics, Quantum Theory or Relativity have known only limited success

. To summarize, the Maxwell Demon is a thought experiment which calls into question the axiomatic foundations of a subject for which, to date, there are no axioms. Note that the 4 "Laws" of Thermodynamics are not axioms: no-one has ever shown that they are either independent, consistent or complete.

From his historical recapitulation of the restatements of the Maxwell Demon by von Clausius, Boltzmann, Landauer, Bennett, Szilard, and Feynman, Callender concluded that they all use the Second Law as a premise for deducing the Second Law. The Maxwell Demon thought experiment has led to the discovery of a close connection between Thermodynamics with Information Theory, through a common notion of Entropy. Nowadays, following Brillouin, most "explanations" of the paradox are based on Information Theory.

Following Callender's talk there was a reception on the outdoor terrace of the Kroc Center. I sat down at a table with the delegates from Charles University in Prague. Altogether there were 7 delegates from the Czech Republic at the conference . Among them was Mrs. Raji Hrovoska, from India but married to Mr. Hrovosky, who runs a research institute in Prague. She comes from a prominent family of scientists and is related to both Raman and Chandrasekhar.

We were told that if we stayed around until 9:45 we would be seeing fireworks from Seaworld, the neighboring whale and dolphin circus which has ties with USD . Most of us were tired, only a few remained to watch, and I did not stay around.

Plenary Talk
9 AM Monday, July 29th
Marlan O. Scully (Texas A&M)
"Quantum Thermodynamics: From Quantum Heat Engines to Maxwell's Demons and Beyond"

From M.O. Scully's abstract:

" ...thermodynamics was the mainspring of quantum theory. Some think the time is ripe for quantum mechanics to return the favor by challenging the foundations of thermodynamics...In a classical Carnot cycle engine the efficiency of converting heat to work is determined solely by the temperatures Th and Tc of the hot and cold reservoirs. However in quantum thermodynamics the quantum phase provides a new and interesting control parameter. For example, with properly chosen quantum phase, it is possible to extract work even when Th = Tc. However the second law of thermodynamics is not violated. The present photon-Carnot quantum heat engine provides a simple model for studying various quantum effects in thermodynamics. "

Scully is a tall, slender man, elderly but appears to be in his 50's, and in excellent condition . An international authority on quantum optics and a member of the National Academy of Sciences, his view of the subtleties of this subject is exceptionally lucid. In 1992 he coined the term "phaseonium" This is a new form of matter in which the quantum atomic phase is held fixed for long times compared with various relaxation processes. He is also associated with the development of the phaser, or phaseonium laser: a kind of laser without inversion (LWI) that creates quantum coherence via Electromagnetically Induced Transparency (EIT) .

On the blackboard Scully wrote down a list of 7 directions in which one ought to proceed in designing experiments to challenge the Second Law:

  1. The Negentropy theory of Norman Ramsey. A theory of negative temperatures developed in 1956 , when Ramsey was working on Nuclear Magnetic Resonance, it provides the theoretical framework for situations in which heat can be completely transformed into work.

  2. The Ellipsoid Paradox. Scully drew a schematic of an ellipsoid, placed radiating atoms at its foci, A and B, and affixed a sphere at one end. This represents an experiment arrangement in which atoms become colder at B and heat up at A. Scully thinks there is no real paradox here. In 1982 someone from Fermi Labs made the argument that this thought experiment depends on "point particles", and that the seeming paradox is resolved when they are replaced by real ones. Scully admitted that the experiment has never been done.

  3. Quantum Coherence. Slowing down the speed of light. At present it can be brought down to 1 meter per second. If light can be stopped entirely one might have time reversal, which might be thought to reverse the direction of entropy increase .

  4. Quantum and Classical Maxwell Demons

  5. Theoretical arguments from Information Theory.

  6. The "quantum afterburner" effect. Scully reported that this conception has generated an exceptional amount of positive and negative criticism. The idea is that by using a combination laser-internal combustion engine hybrid system overall energy efficiency can be increased. Scully and his crew in Texas are setting up experiments to demonstrate this. Phaseonium Lasers might supply the "Super-Carnot fuel" which would go into this engine.

  7. In other word, Scully argued that by using quantum coherence to break detail balance between absorption and emission, it is possible to extend the insights of Carnot and extract energy from a single heat bath without violating the 2nd Law of Thermodynamics.

Plenary Talk
Afternoon Session, Monday July 29th 1:30
David Albert, (Columbia u.)
"Maxwellian Demons and the Meaning of Entropy"

Albert began his talk by making the argument that thermodynamic entropy must apply to individual systems rather than to ensembles. In his fashion he flatly stated that all other points of view are wrong. Ergodicity also he sees as irrelevant. ( this is the working hypothesis normally required to connect Thermodynamics to Statistical Mechanics: it states that the long-term energy time averages of complete ensembles are identical to those of individual systems. )

His interpretation of the Maxwell Demon paradox was well stated . Combining the Demon with the system itself to produce a hyper-system, he asked us to imagine that the actions involved in separating out the fast from the slow molecules has the effect of "disassociating" the demon itself , giving it two distinctive states, thereby greatly increasing the total entropy of the hyper-system.

According to Albert Liouville's Theorem ( Invariance of the phase-space volume of an ensemble under a Hamiltonian flow) is all that one really needs to show that Entropy cannot decrease. He admitted that this is insufficient to show why it must increase. Following that his delivery became so wrapped up in hypotheticals, vague meanderings, ifs, buts and maybes, that it was impossible to follow him further.

During the question period, V. Chapek ( Charles University, Prague) , gave his opinion that Caratheodory's Theorem refuted all of Albert's arguments. This is a Theorem of pure mathematics, ( theory of Integral Equations) , which can be used to show that inaccessible states exist in the neighborhood of any given state of a closed thermodynamic system. Chapek did not elaborate on how Caratheodory's beautiful result invalidated the assertions of David Albert. Nor did he specify which of his numerous assertions were being invalidated.

Monday 2:15 Afternoon Sessions:
Larry S. Schulman ( Clarkson u.)
" Opposite Thermodynamic Arrows of Time"

Schulman's books reflect his on-going concern with the relationship between the Second Law and the arrow of time. Many contemporary physicists ( see for example Hawking in "Brief History of Time") relate the arrow of time to 3 distinct phenomena :

  1. The direction of living consciousness and thought;

  2. The direction of increasing entropy, which is a way of stating the second law, and

  3. The direction of the expansion of the universe and Hubble's Law.

As a general rule, they avoid speaking of the direction of Causation itself because all of the other laws of physics are time reversible.

Schulman's talk was about the possible connections between (2) and (3) : what happens to the Second Law of Thermodynamics in cosmological models , in which there is a Big Bang at the beginning of universal time and a Big Crunch at the other end? If the direction of the Second Law is linked to the expansion of the universe, then it stands to reason that there will be a time-reversal of the Second Law after the expansion ceases, and the contraction leading to the Big Crunch begins. In other words, somewhere in between the beginning and the ending of the universe there is a period in which two arrows of time are simultaneously present.

The 1st Arrow, which we call the Second Law, goes from "order" to "disorder". The Second Arrow therefore goes from "disorder" to "order" . ( The pieces and contents of the broken glass of orange juice do pick themselves up and return to the table !)

Using a schematic and simplified model from the theory of Dynamical Systems, ( physicists call these "toy models") , Schulman elaborated a picture of what might happen if one lived in a world in which the two arrows of time were operative together. One then finds all the phenomena of Chaos Theory present in real physical systems: periodic cycles of transformation between work and heat ( perpetual motion engines of the second kind) , stationary "fixed point" systems, chaotic turbulence in which the concept of entropy no longer has any meaning. In his scheme all these phenomena emerge in a relatively short span of time.

If we are in fact poised between a Big Bang and a Big Crunch , there will come a time in which all of these phenomena will be visible in the world around us. If some of them are present in today's world, one might be able to use them to estimate how long the universe is destined to last.

During the question period at the closing forum on the last day of the conference, Thursday, August 1, Schulman presented about as satisfactory a description of the distinction between "heat" and "work", as any that I'm aware of.

"Heat", he said, merely means the sum total of all the inaccessible degrees of freedom in a system, whereas "Work" stands for the accessible degrees . The sum total of all degrees of freedom goes into the measurement of energy, which is invariant. By finding ways to access more degrees of freedom one can shift the balance between heat and work.