Group entropies: A new family of information measures for complex systems

Titulo:  “Group entropies: A new family of information measures for complex systems”

Ponente: Piergiulio Tempesta, Universidad Complutense de Madrid and Instituto de Ciencias Matemáticas (ICMAT) – Madrid

 Organizador: José María Amigó García

Fecha: Viernes 25 de enero de 2019, 12:00 h.

Lugar: Sala de Seminarios, Instituto Universitario de Investigación CIO, Edificio Torretamarit, Universidad Miguel Hernández (Campus de Elche)

Resumen: We will show that an intrinsic group-­theoretical structure is at the heart of the notion of generalized entropy. This structure emerges when imposing the requirement of composability of an entropy with respect to the union of two statistically independent systems. A new formulation of the celebrated Shannon-­Khinchin set of axioms is proposed, obtained by replacing the additivity axiom with that of composability.

The theory of formal groups offers a natural language for our group-­theoretical approach to generalized entropies. In this settings, the known entropies can be encoded into a general trace-form class, the universal-group entropy (so called due to its relation with the Lazard universal formal group of algebraic topology).

We shall also prove that Renyi’s entropy is the first example of a new family of non trace-form entropies, of potential interest in the theory of complex systems, called the Z-entropies. Each of them is composable and, in particular, generalizes simultaneously the entropies of Boltzmann and Renyi (obtained under suitable limits).

In particular, we will show that complex systems can be classified into universality classes, each characterized by a specific phase space growth rate, and described by a suitable group entropy adapted to it.