Stephen P. King (stephenk1@home.com)
Fri, 12 Mar 1999 06:24:56 -0500
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Date: Thu, 11 Mar 1999 19:27:44 -0800 (PST)
From: Chris Hillman <hillman@math.washington.edu>
To: "Stephen P. King" <stephenk1@home.com>
Subject: Re: Information Mechanics
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Hi, I am not sure if this some sort of mailing list or if I should reply
to all recipients.
> I just cut and pasted this from the bionet.info-theory newgroup. Chris
> comes thru again! :) I am particularly interested in the discussion of
> connections and curvature (and the tacit ideas of metrics involved).
I just tried and failed to come up with some references to the work on
"statistical manifolds".
However, entropy seems to be a concept which can be reformulated in an
incredible variety of ways, and for another connection between entropy and
geometry (of horocyles in hyperbolic geometry), see the paper by Gerard
Knieper, Ergodic Theory & Dynamical Systems 17 (1997) 1131-35, which
discusses a "Liouville entropy".
> I am trying to acces the papers mentioned but my local servers are
> down. I'll keep trying. :) Anyway, I am becoming convinced that
> Hitoshi's point of not defining a unique connection between the Local
> Systems (mapped via fiber bundles to a Riemannian mainfold) may need
> some clarification.
Huh? ;-) I take it this was part of a mailing list discussion?
Chris Hillman
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