Entropy modulo a prime
Year: 2019
Type: preprint
Abstract: Building on work of Kontsevich, we introduce a definition of the entropy of a finite probability distribution in which the "probabilities" are integers modulo a prime p. The entropy, too, is an integer mod p. Entropy mod p is shown to be uniquely characterized by a functional equation identical to the one that characterizes ordinary Shannon entropy. We also establish a sense in which certain real entropies have residues mod p, connecting the concepts of entropy over R and over Z/pZ. Finally, entropy mod p is expressed as a polynomial which is shown to satisfy several identities, linking into work of Cathelineau, Elbaz-Vincent and Gangl on polylogarithms.
Source: arXiv (Cornell University)
Author: Leinster, Tom
Institution: University of Edinburgh
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G1847744412
OpenAlex ID: W4301431545