Thermodynamic semirings

Matilde Marcolli, Ryan Thorngren
2014 Journal of Noncommutative Geometry  
Thermodynamic semirings are deformed additive structures on characteristic one semirings, defined using a binary information measure. The algebraic properties of the semiring encode thermodynamical and information theoretic properties of the entropy function. Besides the case of the Shannon entropy, which arises in the context of geometry over the field with one element and the Witt construction in characteristic one, there are other interesting thermodynamic semirings associated to the Rényi
more » ... d Tsallis entropies, and to the Kullback-Leibler divergence, with connections to information geometry, multifractal analysis, and statistical mechanics. A more general theory of thermodynamic semirings is then formulated in categorical terms, by encoding all partial associativity and commutativity constraints into an entropy operad and a corresponding information algebra.
doi:10.4171/jncg/159 fatcat:34z6lt2tbjhkdooi5ois6s5iye