Exact distribution functions in two‐dimensional lattice polymers. Comparison with maximum entropy distributions

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Abstract
Toeplitz matrices are used to calculate the complete distribution functions for such quantities as the fraction of a particular conformational state and the end‐to‐end distance in 2‐dimensional lattice polymer models with a finite range of intrachain correlation. These are compared with approximate distribution functions obtained using the maximum entropy principle. The two‐parameter maximum entropy distribution (giving the exact first and second moments) in most cases gives a good approximation to the exact distribution and always gives a better approximation than a simple Gaussian approximation. We illustratesome extreme forms of the distribution functions when the intrachain interactions are either very attractive or very repulsive.