Entropies, Zeta Functions and Complex Systems

Description
In this talk several connections between statistical mechanics and number theory will be illustrated. It will be shown that a class of generalized entropies from one side, and L-functions and generalized zeta functions from the other side, can be closely related by means of the theory of formal groups. Indeed, nonadditive entropies, relevant in many contexts of nonequilibrium thermodynamics can be defined from realizations of the multiplicative, Euler, Abel formal groups, as well as infinitely many new entropic functionals. At the same time, one can associate a class of generalized Riemann-type zeta functions from realizations of Lazard's universal formal group.A class of scale-free complex networks will also be constructed in connection with the theory of multiplicative zeta functions.
Organised by Prof. A. Pluchino