标题： 聚合物构象通过接触矩阵粗粒化的信息丢失 显示英文标题

标题： Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

摘要： 接触矩阵提供了Z^n上一条线性链（聚合物或随机游走）的构型ω的粗粒化描述：当第i步和第j步的位置距离小于或等于某个距离"a"时，C_{ij}(ω)=1，否则C_{ij}(ω)=0。 我们考虑长度为N的聚合物模型，其权重对应于简单随机游走（SRW）和自避游走（SAW），其中"a"是最小允许的距离。 我们证明，在N的主阶项下，接触矩阵的数量与SRW的游走数量相等，但不与SAW的游走数量相等。 对于n ≤ 2，SRW的粗粒化香农熵与细粒化香农熵一致，但对于n ≥ 3则不同。 显示英文摘要

摘要： 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.