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Thermal Physics 15.1

``A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts.'' -- A. Einstein
 
``But although, as a matter of history, statistical mechanics owes its origin to investigations in thermodynamics, it seems eminently worthy of an independent development, both on account of the elegance and simplicity of its principles, and because it yields new results and places old truths in a new light in departments quite outside of thermodynamics.''
-- J.W. Gibbs

We have seen how a few simple laws (in particular NEWTON'S SECOND LAW) can be combined with not-too-sophisticated mathematics to solve a great variety of problems - problems which eventually are perceived to fall into a number of reasonably well-defined categories by virtue of the mathematical manipulations appropriate to each - and that those distinct classes of mathematical manipulations eventually become familiar enough to acquire familiar names of their own, such as ``conservation of impulse and momentum'' or ``conservation of work and energy'' or ``conservation of torque and angular momentum.'' This emergence of new tacit paradigms was the great conceptual gift of the Newtonian revolution. But the most profound practical impact of the new sciences on society came in the form of the Industrial Revolution, which was made possible only when the science of mechanics was combined with an understanding of how to extract usable mechanical work from that most mysterious of all forms of energy, heat. Historically, heat was recognized as a form of energy and temperature was understood in terms of its qualitative properties long before anyone truly understood what either of these terms actually meant in any rigorous microscopic model of matter. The link between Newton's mechanics and the thermodynamics of Joule and Kelvin was forged by Boltzmann long after steam power had changed the world, and a simple understanding of many of the finer points of Boltzmann's statistical mechanics had to wait even longer until Quantum Mechanics provided a natural explanation for the requisite fact that the number of possible states of any system, while huge, is not infinite, and that small, simple systems are in fact restricted to a countable number of discrete ``stationary states.'' In this drama Albert Einstein was to play a rather important role. The following conceptual outline of Statistical Mechanics is designed to make the subject as clear as possible, not to be historically accurate or even fair. Having made this choice, however, I hope to be able to display the essence of the most astonishing product of human Science without undue rigamarole, and perhaps to convey the wonder that arises from a deeper and more fundamental understanding.


 
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Next: Random Chance
Jess H. Brewer
1998-11-22