 02514 Patrik L. Ferrari, Joel L. Lebowitz
 Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices
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Dec 11, 02

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Abstract. Contact matrices provide a coarse grained description of the
configuration $\omega$ of a linear chain (polymer or random walk) on
$Z^n$: $C_{ij}(\omega)=1$ when the distance between the position
of the $i$th and $j$th step are less then or equal to some distance
$a$, $C_{ij}(\omega)=0$ otherwise. We consider models in which
polymers of length $N$ have weights corresponding to simple and
selfavoiding random walks, SRW and SAW, with $a$ the minimal
permissible distance. We prove that to leading order in $N$, the
number of matrices equals the number of walks for SRW but not SAW.
The coarse grained Shanon entropies for SRW agree with the fine
grained ones for $n \leq 2$ but disagree for $n \geq 3$.
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