Modes, modals, and barycentric algebras: a brief survey and an additivity theorem
Jonathan D. H. Smith · Demonstratio Mathematica · 2011
Abstract Modes are idempotent and entropic algebras. Modals are both join semilattices and modes, where the mode structure distributes over the join. Barycentric algebras are equipped with binary operations from the open unit interval, satisfying idempotence, skew-commutativity, and skew-associativity. The article aims to give a brief survey of these structures and some of their applications. Special attention is devoted to hierarchical statistical mechanics and the modeling of complex systems. An additivity theorem for the entropy of independent combinations of systems is proved.