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.

Back to the course page on "Statistical Mechanics and Thermodynamics" by F. Nori.

Web page created by F. Nori.