Benford's Law from Turing Ensembles and Integer Partitions

In this paper we investigate the information-theoretic and mathematical foundations of Benford's law, an important case of a statistical relationship that appears to constrain the information-theoretic behavior of numbers. In the present analysis we seek to deduce a general cause for Benford-like distributions to arise. We posit that they both follow from optimality and renormalization as applied to information-theoretical functionals. We also perform computational experiments that corroborate our conclusions.