Maximum-entropy calculation of end-to-end distance distribution of force stretching chains

Using the maximum-entropy method, we calculate the end-to-end distance distribution of the force stretched chain from the moments of the distribution, which can be obtained from the extension-force curves recorded in single-molecule experiments. If one knows force expansion of the extension through the $(n-1)$th power of force, it is enough information to calculate the $n$ moments of the distribution. We examine the method with three force stretching chain models, Gaussian chain, free-joined chain and excluded-volume chain on two-dimension lattice. The method reconstructs all distributions precisely. We also apply the method to force stretching complex chain molecules: the hairpin and secondary structure conformations. We find that the distributions of homogeneous chains of two conformations are very different: there are two independent peaks in hairpin distribution; while only one peak is observed in the distribution of secondary structure conformations. Our discussion also shows that the end-to-end distance distribution may discover more critical physical information than the simpler extension-force curves can give.