Metric-Entropy Pairs on Lattices

Dan Simovici (University of Massachusetts Boston, USA)

Abstract: We introduce the notion of ∧- and ∨-pairs of functions on lattices as an abstraction of the notions of metric and its related entropy for probability distributions. This approach allows us to highlight the relationships that exist between various properties of metrics and entropies and opens the possibility of extending these concepts to other algebraic structures.

Keywords: entropy, metric, modular lattice

Categories: H.1.1, H.2.8