Shannon and joint entropy are recast as sums of infinitesimal dilogarithm brackets, and the five-term dilogarithm is deformed to the four-term infinitesimal dilogarithm via dual numbers.
Foam cobordism and the Sah-Arnoux-Fathi invariant
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abstract
This is the first in a series of papers where scissor congruence and K-theoretical invariants are related to cobordism groups of foams in various dimensions. A model example is provided where the cobordism group of weighted one-foams is identified, via the Sah-Arnoux-Fathi invariant, with the first homology of the group of interval exchange automorphisms and with the Zakharevich first K-group of the corresponding assembler. Several variations on this cobordism group are computed as well.
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Diagrammatics of information
Shannon and joint entropy are recast as sums of infinitesimal dilogarithm brackets, and the five-term dilogarithm is deformed to the four-term infinitesimal dilogarithm via dual numbers.