On 10/11/13 2:00 PM, Nick Thompson wrote:
At Friam today, we had our first discussion of entropy in a while.
It was like old times. I really enjoyed it.
But the following disagreement came up. I am, I think, a bit of what
philosophers call an essentialist. In other words, I assume that when
people use the same words for two things, it aint for nothing, that
there is something underlying the surface that makes those two things
the same. So, underlying all the uses of the word "entropy" is a
common core, and .... Here's the tricky bit ... that */that common
core could be expressed mathematically/*. However, I thought my
fellow discussants disagreed with this naïve intuition and agreed that
the physical and the information theoretical uses of the word
"entropy" were "not mathematically equivalent", which I take to mean
that, no mathematical operation could be devised that would turn one
into the other. That the uses of the word entropy were more like
members of a family then they were like expressions of some essence.
I wonder what you-all think about that.
/He's Baaack! /
I think your question, whether naive (as you seem to suggest) or deeply
astute is good for us to consider. To the extent that we share a common
interest in "complex systems", I believe that the regimes of
Shannon/Information Entropy, Gibbs/Thermodynamic Entropy, and
vonNeumann/QM entropy overlap in non-ergodic systems... I think that
the biggest distinction between these measures of entropy occur in
near-equilibrium systems where the ergodic hypothesis is (most) relevant.
Our patron Saint Guerin likes to invoke Spontaneous Symmetry Breaking
which I believe is a consequence or indication of the ergodic hypothesis
being broken in macroscopic systems.
As our technologists move further and further into the nano scale realm,
designing and building systems at the atomic or molecular level, we will
see a stronger practical overlap of Shannon and Gibbs (and Von Neumann?)
entropy.
I *do* look forward to a rousing round of discussion on the topic here.
Welcome back,
- Steve
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