Ian Wark Research Institute,
University of South Australia, Mawson Lakes SA 5095 Australia.
in 'Statistical Physics on the Eve of the Twenty-First Century', M.T. Batchelor and L.T. Wille (eds), (World Scientific, Singapore, 1999).
Abstract
The role that entropy plays in information theory is described,
together with a pedagogic derivation of Gibb's formula
that expresses it in terms of the probability of states.
It is then shown how the entropy of a spin lattice system may be
expanded
in terms of successively higher order spin correlation functions.
This expansion is based on a Markov approach
and it has previously proven successful in one dimensional
spin-lattice systems,
which have possible applications to time series and signal processing.
Here the procedure is generalized to higher dimensions,
where it may be applicable to image analysis and tomography.
Tests for the two-dimensional Ising model show that two terms
of the expansion suffice for accurate result at both high and low
temperatures.
The corresponding Markov superposition approximation
for the higher order correlation functions
in terms of elemental adjacent correlation functions
(i.e. between neighbor vertices, bonds, and squares),
is given in both two- and three-dimensions.
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