02-514 Patrik L. Ferrari, Joel L. Lebowitz

Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices (334K, Postscript) 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 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 $n \geq 3$.

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