A comment on Rivier's maximum entropy method of statistical crystallography

Abstract

In the literature, Rivier's maximum entropy method was used to prove Lewis' law and a linear Aboav's law. In this paper we show that the functional forms of these two laws for a statistically equilibrated cellular network, even if such a network really exists, cannot be derived or proved by this method. For example, within the maximum entropy method, we demonstrate that a quadratic Aboav's or Lewis's law is as probable as a linear one.