Information loss in coarse graining of polymer configurations via contact matrices

Patrik L Ferrari, Joel L Lebowitz
2003 Journal of Physics A: Mathematical and General  
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
more » ... umber 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.
doi:10.1088/0305-4470/36/21/303 fatcat:rkfsrnbnuvgs7g3pgrc4kamzya