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Modes, modals, and barycentric algebras: a brief survey and an additivity theorem

Smith J. D. H.

Demonstratio Mathematica

2011

Vol. 44, nr 3

571-587

Modes are idempotent and entropic algebras.Modals are both join semi lattices and modes,where the mode structure distributes over the join.Barycentric algebras are equipped with binary operations from the open unit interval,satisfying idempo tence,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 hierar chical statistical mechanics and the modeling of complex systems.An additivity theorem for the entropy of independent combinations of systems is proved.