Patrik L. Ferrari, Joel L. Lebowitz
Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices
(334K, Postscript)

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 
self-avoiding 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 $n \geq 3$.