Entropy algebras and Birkhoff factorization

Abstract

We develop notions of Rota–Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deformations arising from quantum information measures such as the von Neumann entropy. We consider examples related to Manin's renormalization and computation program, to Markov random fields and to counting functions and zeta functions of algebraic varieties.

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© 2015 Elsevier B.V. Received 23 December 2014; Accepted 14 July 2015; Available online 22 July 2015. The first author is supported by NSF grants DMS-1007207, DMS-1201512, PHY-1205440. The second author was supported by a Summer Undergraduate Research Fellowship at Caltech and by the Rose Hills Foundation.

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Submitted - 1412.0247v1.pdf

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