From: "C. Hillman" <optimist@u.washington.edu>
Newsgroups: sci.math,sci.physics
Subject: Re: Information Theory - a bit of information - at the quantum level
Date: Wed, 3 Jun 1998 19:32:06 -0700

On 4 Jun 1998, Mike wrote:

> Entropy is defined as Q/T, where Q is the energy entering the system, and T
> is the temperature of the system.

This is the thermodynamical definition; even with physics there are
statistical mechanical definitions, and the relationship between these
various statistical mechanical approaches (Gibbs vs. Boltzmann) and the
thermodynamical approach is rather subtle.

There are also numerous "mathematical" concepts of entropy, i.e.
quantities defined in various abstract settings.  These abstract contexts
may involve concepts from probability theory, combinatorics, graph theory,
functional analysis, group actions, manifold theory, topology, the theory
of algorithms, symbolic dynamics, etc.  See for instance my page

 http://www.math.washington.edu/~hillman/entropy.html

for some hint of the variety of different "entropies".
 
> Is the definition of entropy valid at the quantum level of physics?

Not the one you gave, of course, but there are both classical and quantum
statistical mechanical definitions of physical entropy.  A particularly
simple example of the latter would be von Neumann's entropy operator.

Chris Hillman

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