"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.

- Random Chance
- Counting the Ways
- Statistical Mechanics
- Temperature
- Time & Temperature
- The Boltzmann Distribution
- Ideal Gases
- Things I Left Out

1998-11-22