Maximum Entropy and Equations of State for Random Cellular Structures.

摘要

Random, space-filling cellular structures (biological tissues, metallurgical grain aggregates, foams, etc.) are investigated. Maximum entropy inference under a few constraints yields structural equations of state, relating the size of cells to their topological shape. These relations are known empirically as Lewis's law in Botany, or Desch's relation in Metallurgy. Here, the functional form of the constraints is now known as a priori, and one takes advantage of this arbitrariness to increase the entropy further. The resulting structural equations of state are independent of priors, they are measurable experimentally and constitute therefore a direct test for the applicability of MaxEnt inference (given that the structure is in statistical equilibrium, a fact which can be tested by another simple relation (Aboav's law)). 23 refs., 2 figs., 1 tab.