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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 Rényidoi:10.4171/jncg/159 fatcat:34z6lt2tbjhkdooi5ois6s5iye