Second Law Conference 2

Morning Plenary Session Tuesday, July 30th
Daniel C. Mattis (university of Utah)
" The Second Law of Thermodynamics as a Purely Local Phenomenon"

From Mattis' abstract:

" I .... examine the optimal state of a single particle that interacts with a quantum field by a momentum-conserving interaction. I again find the optimal wave function to consist of a Gaussian ( i.e. Maxwellian) distribution of momenta, regardless of the state of excitation of the quantum field. In this last instance the 'effective temperature' at which the designated particle achieves its equilibrium is determined purely by the strength of the interaction parameter, and not by the degree of excitation of the external field ... "

In his talk Mattis elaborated several paradoxes associated with the so-called "thermalization" of a system: increasing the levels of disorder , ( either in a single system, or ensemble of systems, or even a single point-particle) until its dynamics can no longer be described by Hamiltonian or deterministic mechanics. Four paradigms were presented :

  1. Pair particle creation/annihilation in Quantum Electrodynamics. The expression for the Hamiltonian equation, ( which expresses the energy in terms of (generalized) positions and momenta) contains no Thermodynamics, Therefore this system cannot be thermalized. This result was already known to Einstein and Planck at the turn of the century.

  2. The thermodynamics of the propagation of sound. The standard model from elasticity and thermodynamics is unrealistic unless one includes certain extraneous terms to account for the decay of the wave. This is in violation of classical Thermodynamics.

  3. Picture a system consisting of a huge number of tiny beads pierced by a circular metal ring. The beads move with momenta distributed according to some random scheme. By the Conservation of Momentum the distribution will be globally invariant . However, the distribution of the velocities of a single particle , owing to collisions with its neighbors, (which collide with their neighbors, etc.,) is highly thermalized.

    Hence, individual particles are thermal, whereas the global system is mechanical. The system is known as "Tonk's Gas" . See Mattis' article in "The Many-Body Problem", World Publishing Co., 1994.

  4. The "Snowball" Model. Imagine a single point-particle P of mass M, in a thermalized quantum bath, consisting of myriads of very light particles of mass m << M. P moves through space picking up electrons and throwing off quanta, in the manner of a snowball. Eventually its accumulated weight will slow it down to rest or to an equilibrium state.

To quote from Mattis' paper "Thermal Equilibrium as a Local Phenomenon": " The massive particle , perforce, absorbs not just the mass of the light-weight particle but also its momentum. Energy is conserved via an isotropic radiation field that englobes the system; exothermic reactions radiate the excess energy, endothermic ones absorb ambient radiation, both instantaneously ....

" This model is a microscopic version of the cartoonish snowball or avalanche rolling down a snowy slope, gathering size, mass and momentum as it goes."

Sessions, Tuesday Morning 11 AM

  1. My own paper was delivered at this session. Click on Counter-Intuitive.

  2. Stacey Langton, Historian of Science.
    "What Did Carnot Say About the Second Law?"

    Since most historians practice substandard science - the notable exceptions are thereby all the more to be valued - and since most scientists carry about with them a comicbook-level understanding of the history of their field, it is refreshing to find someone who performs tolerably in both disciplines. Although there were no astounding revelations in Langton's talk, it was enjoyable on its own terms. Quoting from the abstract:

    " The science of Thermodynamics was founded by Sadi Carnot [.....] in 1824. Carnot's work was based on the incorrect principle of conservation of heat. The concept of entropy was first adumbrated by Rankine, in 1850, 18 years after Carnot's death. An explicit statement of a 'Second Law' was first given four years later by Clausius. It is sometimes said, nevertheless, that 'Carnot knew the Second Law without knowing the First.' In this talk we will examine Carnot's actual argument, in order to determine whether, or to what extent, Carnot 'knew the Second Law'." Langton's conclusion is that the 'Carnot Principle' based on the Caloric theory, allowed for the possibility of perpetual motion machines of the second kind. It was von Clausius who, by discarding the caloric theory, then looking at what Carnot had written , extracted the 'Carnot General Axiom', which leads to the Second Law.

  3. Raji Heyrovska: A Concise Equation of State for Gases Incorporating Thermodynamic Laws

    From the Abstract: "...the author has incorporated the fundamental experimental property, namely heat capacity, into her earlier concise equation of state for gases based on free volume and molecular association/dissociation....This work brings a new, simple, mathematically consistent presentation of the 1st and 2nd thermodynamic laws, internal energy (E), enthalpy (H), Gibbs(G) and Helmholtz(A) free energies and, most importantly, a new insight into the concept of entropy (S) and reversibility...Experimental and calculated heat capacities are correlated with molecular association, using date for nitrogen as an example."

Sessions , Tuesday Morning

    Ken Sekimoto: (Tokyo u. ): Irreversibility Resulting From Contact with a Heat Bath Caused by the Finiteness of the System

    Quote: "Frankly, I'm looking for a job. My English is not too good. However my paper is written in good English". His talk was incomprehensible from beginning to end. Followed by :

  1. Horoaki Yamada ( Niigata u. ) : Dynamically Delocalized State and Classicalization

    Yamada is a tall man. During his talk he stood directly in front of his screen. His transparencies ( what one could see of them) were all covered with very faint and illegible scribbling. The pages themselves were yellowed and completely reflected the light, making it impossible to see anything. There was also the usual language barrier in speaking English.

    Nobody followed anything in his talk after the first two minutes.

Dinner at the Catamaran restaurant, on the beachfront in back of hotel in downtown San Diego.

Surf, surfers, bonfires, fake Hawaiian music, fabulous Mexican buffet. Dinner in the company of a Romanian physicist who's been doing research at some institute in Mexico for the last 10 years, and 3 well-read Italians. We spoke about books, opera, history, city planning, Churchill, the Pope.

Plenary Session 9 AM
Wednesday Morning, July 31st
Jos Uffink ( Utrecht u.)
Irreversibility and the Second Law of Thermodynamics

The term Irreversibility actually refers to 3 different notions:

  1. A process may be considered reversible if every state of a system S between time t = 0 and t = T is attained by a reverse process . Example: the pendulum swings back through its trajectory to its initial position. Thus, the state variables of position and energy are recovered, while momentum is reversed. A reverse process therefore generally comes about through reversing the directions of the momenta.

  2. Rather than speaking of reversibility, Max Planck was concerned with situations in which a given state is recoverable : that is to say, given position, energy and momentum of a system S at time t = 0 , there is a process whereby this combination of states can be realized at some future time T.

  3. von Clausius uses the word 'reversible' in the sense of quasi-static, change which in theory, proceeds so slowly that a system can move from equilibrium state to equilibrium state along its entire trajectory. They are reversible in the sense that one can jump back and forth along an infinitesimal increment in the state variables.

    Quasi-static reversibility is somewhat theoretical and abstract. Uffink calls it a 'limit condition' and consigns it to the domain of thought experiments.

    As examples of the application of these different notions of reversibility, Uffink showed slides on which he had drawn various engines that exemplify them:

    1. Isothermal Expansion ( Steam Engine): recoverable, quasi-static.

    2. Joule's paddle wheel experiment: non-recoverable, non-quasi static

    3. Sommerfeld's experiment. This is a thought experiment : A condenser is attached to a resistor sitting in a heat bath. Because of the incremental accumulation of resistance, the condenser periodically discharges: quasi-static, non-recoverable

    4. The simple Harmonic Oscillator: recoverable, non quasi-static.
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