ENTROPY ALGEBRAS AND BIRKHOFF FACTORIZATION

Abstract

Abstract. We develop notions of Rota–Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deforma-tions 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. 1