On Sun, Feb 05, 2012 at 07:28:47PM +0100, Evgenii Rudnyi wrote:
> The most funny it looks in the conclusion
> 
> p. 28(142) "First, all notions of entropy discussed in this essay,
> except the thermodynamic and the topological entropy, can be
> understood as variants of some information-theoretic notion of
> entropy."
> 
> I understand it this way. When I am working with gas, liquid or
> solid at the level of experimental thermodynamics, the information
> according to the authors is not there (at this point I am in
> agreement with them). Yet, as soon as theoretical physicists start
> thinking about these objects, they happen to be fully filled with
> information.
> 
> Evgenii

Would you say that thermodynamic entropy is the same as the
Bolztmann-Gibbs formulation? If not, then why not? You will certainly
be arguing against orthodoxy, but you're welcome to try.

If you agree that it is the same, then surely you can see that
information and entropy are related - they are both the logarithm of a
probability - in the case of Boltzmann it is the logarithm of the
number of possible microstates multiplied by the probability of the
thermodynamic state.

Are you aware of the result relating the Kolmogorov "program length"
complexity measure to the logarithm of the probability of that program
appearing in the universal prior?

Both are examples of information, but measured in different contexts.

I will comment on the entropy context of the JANAF tables in another
post. Essentially you are asserting that the context of those tables
is the only context under which thermodynamic entropy makes sense. All
other contexts for which there is an entropy-like quantity do not
count, and those measures should be called something else. A variety
of information, or complexity perhaps.

Alternatively, we could recognise the modern understanding that these
terms are all essentially equivalent, but that they refer to a family
of measures that vary depending on the context.

It comes down to a terminological argument, sure, but your insistence
that thermodynamic entropy is a special case strikes me as a baroque
means of hiding the thermodynamic context - one that doesn't engender
understanding of the topic.

-- 

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Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au
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