Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

Details Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

2002-12-11

arxiv.org/abs/math-ph/0212035v2

J.Phys.A: Math. Gen. 36 (2003) 5719-5730

Physics

Mathematical Physics

18 pages, 2 figures, latex2e Main change: the introduction is rewritten in a less formal way with the main results explained i

Scientific paper

10.1088/0305-4470/36/21/303

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 than or equal to some distance "a" and 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 for SAW. The coarse grained Shannon entropies for SRW agree with the fine grained ones for n <= 2, but differs for n >= 3.

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