What is Entropy?

entropy: ** 1)** a measure of the degree of
disorder in a substance or a system: entropy always increases and
available energy diminishes in a closed system; **2)** a
thermodynamic measure of the amount of energy unavailable for useful work
in a system undergoing change. See the Second Law of Thermodynamics.

The thermodynamical notion of entropy was introduced in 1854 by Rudolph Clausius, who built on the work of Carnot. His ideas were later extended and clarified by Helmholtz and others. In the 1870's, Ludwig Boltzmann found a "statistical" definition of entropy which, he claimed, reduced to the earlier notion of Clausius. Around the same time, Josiah Willard Gibbs introduced a slightly different statistical notion of entropy. Here are some pages discussing these ideas:

**The Page of Entropy,**by Dave Slaven (Physics, Saginaw Valley State University) offers a very nice, non-technical introduction to the statistical notion of physical entropy.**How to teach statistical physics,**by Koo-Chul Lee (Physics, Seoul National University, Korea) offers some Java applets illustrating micrononical ensembles, thermal relaxation, fluctuations in entropy, the Maxwell-Boltmann distribution and other good stuff.

Around 1930,
John von
Neumann (inventor of the programmable computer) introduced the *entropy
operator*, which is the analog of numerical entropy for quantum mechanics.
These days, various physicists are attempting to generalize von Neumann's
operator entropy in the context of noncommutative C-* algebras (the mathematical
setting for the rigorous theory of statistical mechanics introduced by Ruelle
and others).

A quick search on google will find a number of sites on Entropy & the Second Law of Thermodynamics.

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Copyright © 2022 Paul Hopkins. All rights reserved.

Revised: 04/22/22.