MEETING THE ENTROPY CHALLENGE: An International Thermodynamics Symposium in Honor and Memory of Professor Joseph H. Keenan
1033(2008); http://dx.doi.org/10.1063/1.2979066View Description Hide Description
Professor Keenan's engineering contributions to thermodynamics, such as the development of the properties of steam, are world‐renowned. His contributions to the science and the teaching of the subject, however, will probably have a longer lasting influence. All of his contributions derived from an uncompromising search for understanding and elimination of ambiguities overlooked or accepted by others. He developed a coherent and logical exposition of the fundamentals of thermodynamics so that the widest possible range of problems could be considered in a uniform and consistent manner. The way Professor Keenan was able to convey to his students but also to his colleagues what he believed about the concepts in thermodynamics, was to ask questions.
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This is the transcript of an interview conducted by Esther Keenan Carr on May 13, 1977, in which Joseph H. Keenan, professor of mechanical engineering at MIT, discusses first his early years and education at MIT, then his career in the mechanical engineering department of MIT, and finally discusses together with George Hatsopoulos how they ended up learning thermodynamics from each other.
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The beginning of thermodynamics was around 1850, when both the first and the second law were formulated. The first law is often formulated as: the energy of the world is conserved and the second law as: the entropy of the world increases. These formulations caught general attention. A lot of what happened until 1912 in understanding these two laws is described in a little book by Paul and Tatania Ehrenfest on “The conceptual foundation of the statistical approach in mechanics” .
A particularly important event was Boltzmann's derivation of the H theorem in 1872 . Even though it soon became clear that this was not a fully acceptable derivation of the second law, it played an important in clarifying what was at stake. Since then much effort has been directed towards this derivation in the context of statistical mechanics. A promising development is dynamic system theory [3, 4]. Prigogine  and the Keenan school [6, 7] advocate introducing irreversibility in the microscopic equations of motion. This would solve the problem without using statistical mechanics. Whether nature works this way should be decided by experiments.
My final conclusion is that in statistical mechanics there is as yet no satisfactory derivation of the second law. On this occasion it seems appropriate to put the derivation of the second law using statistical mechanics as a challenge to the participants of the meeting.
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In this talk, I discuss the mystery of the second law and its relation to quantum information. There are many explanations of the second law, mostly satisfactory and not mutually exclusive. Here, I advocate quantum mechanics and quantum information as something that, through entanglement, helps resolve the paradox or the puzzle of the origin of the second law. I will discuss the interpretation called quantum Darwinism and how it helps explain why our world seems so classical, and what it has to say about the permanence or transience of information. And I will discuss a simple model illustrating why systems away from thermal equilibrium tend to be more complicated.
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I use cosmology examples to illustrate that the second law of thermodynamics is not old and tired, but alive and kicking, continuing to stimulate interesting research on really big puzzles. The question “Why is the entropy so low?” (despite the second law) suggests that our observable universe is merely a small and rather uniform patch in a vastly larger space stretched out by cosmological inflation. The question “Why is the entropy so high” (compared to the complexity required to describe many candidate “theories of everything”) independently suggests that physical reality is much larger than the part we can observe.
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Here I discuss an idea called Maximum Caliber, which provides a useful way to frame problems of non‐equilibrium statistical mechanics. It may be particularly useful for treating small‐numbers situations, such as those that often arise in biology and in nanotech, where the numbers of particles is very small. In analogy with the way the maximization of entropy over microstates leads to the Boltzmann distribution and predictions about equilibria, maximizing a quantity that E.T. Jaynes called “Caliber” over all the possible microtrajectories leads to the dynamical laws such as Fick's law of diffusion and the mass‐action laws of chemical kinetics. The Maximum Caliber method yields dynamical distribution functions that characterize the relative probabilities of different microtrajectories, including “bad actors”, i.e., the microtrajectories that contribute net particle motion in the direction opposite to the macroflux predicted by the Second Law. A potential area of application of Maximum Caliber is modern single‐particle and few‐molecule experiments that can often observe one individual dynamical particle trajectory at a time.
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More insight in the use of thermodynamics and entropy is important to preserve our planet for future generations. We discuss how it may help improve the efficiency of current energy conversion technologies, suggest ways to harness solar energy and develop engines that can generate sustainable carbon‐free energy, and help understand how life and the universe are based on the Laws of Physics.
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In the scientific and engineering literature, entropy—the distinguishing feature of thermodynamics from other branches of physics—is viewed with skepticism, and thought to be not a physical property of matter—like mass or energy—but a measure either of disorder in a system, or of lack of information about the physics of a system in a thermodynamic equilibrium state, and a plethora of expressions are proposed for its analytical representation. In this article, I present briefly two revolutionary nonstatistical expositions of thermodynamics (revolutionary in the sense of Thomas Kuhn, The Structure of Scientific Revolutions, U. Chicago Press, 1970) that apply to all systems (both macroscopic and microscopic, including one spin or a single particle), to all states (thermodynamic equilibrium, and not thermodynamic equilibrium), and that disclose entropy as an intrinsic property of matter.
The first theory is presented without reference to quantum mechanics even though quantum theoretic ideas are lurking behind the exposition. The second theory is a unified quantum theory of mechanics and thermodynamics without statistical probabilities, that is, I am not presenting another version of statistical quantum mechanics.
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The second law of thermodynamics is a cornerstone of physics: together with its companion, the first law of thermodynamics, it is the support on which our scientific understanding of heat and the microscopic motion of atoms and molecules rests. Like Arthur, the once and future king (rex quondam, rex futurus), the second law is always with us, and always will be.
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The Szilard Engine has been used to suggest that the impossibility of an effective Maxwellian Demon is guaranteed by Landauer's Principle in the thermodynamics of computation. Critics suggest that the argument is circular, as Landauer's Principle itself rests upon the assumption that the Second Law is inviolate, and so the impossibility of a Maxwellian Demon remains suspect. We suggest that the correct understanding is that both the failure of the Szilard Engine and the basis of Landauer's Principle are direct, and equivalent, consequences of Hamiltonian dynamics and the normal statistical mechanical assumptions regarding microscopic correlations.
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For a conservative system, during an arbitrary time interval the time‐reversible Hamiltonian equations that describe the motion in the microscopic phase space induce a probabilistic flow in the macroscopic phase space, which is a finite equipartition of the microscopic phase space, whose transition probabilities form a double‐stochastic matrix. As a consequence, the macroscopic entropy at time is larger than or equal to the macroscopic entropy at time Key words: microscopic reversibility, macroscopic irreversibility, generalized H‐theorem.
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Darwinian dynamics is manifestly stochastic and nonconservative, but has a profound connection to conservative dynamics in physics. In this short presentation the main ideas and logical steps leading to thermodynamics from Darwinian dynamics are discussed in a quantitative manner. It suggests that the truth of the second law of thermodynamics lies in the fact that stochasticity or probability is essential to describe Nature.
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Since the first formulations of the second law of thermodynamics there have been very many attempts to derive it from some underlying theory. In the paper at hand we report on results concerning this issue which explicitly require quantum mechanics (rather than classical mechanics) as an underlaying theory. Those results are obtained on the basis of the Hilbert‐space average method.
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In this paper, two points are discussed that are directly or indirectly based on the distinction between two scales of representation of the physical systems: the scale of the individual particles (microscopic scale) and the scale of the macroscopic arrangements. 1) The distinction between work and heat, from which entropy is defined (entropy is the measure of energy that is not associated to work), appears to correspond to the distinction between the macroscopic level (work) and the microscopic level (heat); 2) The problem of time irreversibility is analyzed by examining the working of the equations (mathematical problem) and by examining time construction (philosophical problem). If the mathematical problem appears to us as solved by the observation of the practical behaviour of the systems with a great number of particles (statistical aspect), the philosophical problem remains. One may progress by examining the construction of time in opposition to space, as based on the movement properties of the material points. Neither time, nor space pre‐exist as separate. A cut is made between the points with invariant relations, allowing to define space, and the points with variable relations, allowing to define time. This cut cannot avoid an arbitrary behind which an irreducible or ontological irreversibility is hidden.