ABSTRACT
This chapter is mainly addressed to physicists and engineers with a good knowledge of mathematics. It takes into account the current progresses in pure mathematics and the mental representations often close to emerging engineering issues. The “experimental” confirmation of the Riemann Hypothesis emerges as a minoration of the entropic production and as a maximal scattering of the site of transfer. This analysis made several attempts for approaching the Riemann's Hypothesis from physical analogies of universal mathematical functions, including quantum mechanics using stochastic matrix or self-similar mechanical lattices. The coarse graining between extrema being able to be scaled from a unique law, the main features of ordered lattice is naturally the self-similarity. Closure principles and commutativity of diagrams involve local-global coupling in which construction-partition relationships can then lead specific coarse graining and renormalization opportunities.
