Statistical Mechanics and Thermodynamics

Physics 406. Fall 1998 (Instructor: Prof. Franco Nori. )

A few quotes, and web links, on the history of the subject.

Ludwig Boltzman, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. Perhaps it will be wise to approach the subject cautiously. (Opening lines of "States of Matter", by D.L. Goodstein).

I am conscious of being only an individual struggling weakly against the stream of time. But still remains in my power to contribute in such a way that, when the theory of gases is again revived, not too much will have to be rediscovered. (L. Boltzmann).

But although, as a matter of history, statistical mechanics owes its origins 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).

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).

One should not imagine that two gases in a 0.1 liter container, initially unmixed, will mix, then again after a few days separate, then mix again, and so forth. On the contrary, one finds ... that not until a time enormously long compared to 10^10^10 [10 to the 10th power to the 10th power] years will there by any noticeable unmixing of the gases. One may recognize that this is practically equivalent to never ... (L. Boltzman).

If we wish to find in rational mechanics an a priori foundation for the rpinciples of thermodaynamics, we must seek mechanical definitions of temperature and entropy. (J.W. Gibbs).

The general connection between energy and temperature may only be established by probability considerations. [Two systems] are in statistical equilibrium when a transfer of energy does not increase the probability. (M. Planck).

The laws of thermodynamics may easily be obtained from the principles of statistical mechanics, of which they are an incomplete expression. (J.W. Gibbs).

We are able to distinguish in mechanical terms the thermal action of one system on another from that which we call mechanical in the narrower sense ... so as to specify cases of thermal action and cases of mechanical action. (J.W. Gibbs).

We consider the distribution of the energy U among N oscillators of frequency v [= greek letter nu]. If U is viewed as divisible without limit, then an infinite number of distributions are possible. We consider however---and this is the essential point of the whole calculation--- U as made up of an entirely determined number of finite equal parts, and we make use of the natural constant h = 6.55 x 10^{-27} erg-sec. This constant when multiplied by the common frequency nu of the oscillators gives the element of energy "e" in ergs ... (M. Planck).

So I decided to calculate the spectral distribution of the possible free vibrations for a continuous solid and to consider this distribution as a good enough approximation to the actual distribution. The sonic spectrum of a lattice must, of course, deviate from this as soon as the wavelength becomes comparable to the distances of the atoms ... The only thing which had to be done was to adjust to the fact that every solid of finite dimensions contains an finite number of atoms and therefore has a finite number of free vibrations ... At low enough temperatures, and in perfect analogy to the radiation law of Stefan-Boltzmann ..., the vibrational energy content of a solid will be proportional to T^4. (P. Debye).

Unless otherwise indicated, the quotes above can be found in different chapters of the textbook "Thermal Physics" of Kittel and Kroemer. Second edition. Freeman.

Very short good biographies appear here:
Ludwig Boltzmann,
Josiah Willard Gibbs,
Hermann Ludwig Ferdinand von Helmholtz,
Gustav Kirchhoff,
James Clerk Maxwell, and
Max Karl Ernst Ludwig Planck.
These biographies provide links to dozens of additional ones not listed here (e.g., Bose, Fermi, Ehrenfest, etc., etc.).

A very brief biography of Ludwig Boltzmann.
Ludwig Boltzmann's contributions to physics.

Boltzmann Distribution Software.
Maxwell-Boltzmann's distribution's law.
Lattice Boltzmann Simulations of fluid transport.

The Stefan-Boltzmann radiation law.
Use the Stefan-Boltzmann radiation law to estimate the temperature of Heaven.
Estimate also the approximate temperature of Hell.
On the origin of the Boltzmann factor.

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Web page created by F. Nori.