Evolucion Del Principio De Carnot

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carnot, 7 8 1996

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THE EVOLUTION OF CARNOT'S PRINCIPLE*
E. T. Jaynes** St. John's College Cambridge CB2 1TP, U. K.

Abstract: We trace the development of the technical ideas showing that the Second Law of Ther-

modynamics became, over a Century ago, a general principle of reasoning, applicable to scienti c inference in other elds than thermodynamics. Both the logic and theprocedure of our present maximum entropy applications are easily recognized in the methods for predicting equilibrium conditions introduced by Gibbs in 1875. Chemical thermodynamics has been based on them ever since. What is new in this eld is not the method, but the recognition of its generality. 1. INTRODUCTION 2. CARNOT'S PRINCIPLE 3. FIRST METAMORPHOSIS: KELVIN 4. SECOND METAMORPHOSIS: CLAUSIUS 5.THIRD METAMORPHOSIS: GIBBS 6. FOURTH METAMORPHOSIS: BOLTZMANN 7. CONCLUSION APPENDIX A: COMMENTS ON KELVIN'S RELATION APPENDIX B: ANTI CARNOT ENGINES APPENDIX C: REVERSIBILITY REFERENCES 2 3 4 6 7 8 11 14 15 16 17

*The opening talk at the EMBO Workshop on Maximum Entropy Methods in x ray crystallographic and biological macromolecule structure determination, Orsay, France, April 24 28, 1984.Reprinted in Ericksen & Smith 1988, Vol 1, pp. 267 282 **Visiting Fellow, 1983 84. Permanent Address: Department of Physics, Washington University, St. Louis MO 63130, USA.

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The rst reaction of nearly everybody, on hearing of a mysterious principle called maximum entropy" with a seemingly magical power of extracting more information from incomplete data than they contain, is disbelief.The second reaction, on sensing that there does seem to be something in it, is puzzlement. How is it possible that a quantity belonging to thermodynamics could escape from that setting and metamorphose itself into a principle of reasoning, able to resolve logical ambiguities in situations that have nothing to do with thermodynamics? Newcomers to this eld usually start by asking, not how to apply themethod, or even what numerical results it gives; but I don't see what this has to do with the entropy of thermodynamics is there a connection?" Therefore it might be useful, before seeing details of present applications, to explain that connection. We are taught to think of the First Law of Thermodynamics as a basic law of physics, true of necessity in every case. But attempts to see the SecondLaw in this way Kelvin, Clausius, Planck, Boltzmann and many others never quite succeeded; and Gibbs 1875 recognized that its logic is di erent. He concluded that the impossibility of an uncompensated decrease seems reduced to improbability", a remark that Boltzmann quoted 20 years later in the Introduction to his Gastheorie. Clausius saw the second law as a law of physics, but only aqualitative one a kind of arrow to tell us in which general direction a process will go. Gibbs, while depriving it of that logical certainty, extended its practical application to serve the stronger purpose of quantitative prediction; to ll the logical void left by the great incompleteness of thermodynamic data. Out of all the di erent macroscopic behaviors permitted by the macroscopic data and themicroscopic laws of physics, which should we choose as, not what must happen, but only what will most likely happen? Since Gibbs' Heterogeneous Equilibrium 1875 78 the second law has been used in practice, not as a law of physics", but as a principle of human inference; a criterion for resolving the ambiguities of incomplete data. In this service it does indeed extract more information than could havebeen obtained from the data alone; not by magic but by combining the evidence of the data with the additional information contained in the entropy function. In other words, Gibbs' use of the second law to predict equilibrium states was virtually identical in rationale with our present maximum entropy inference. The experimental con rmation of Gibbs' thermodynamic predictions, and the success of...