Entropy and the spectral action
By Alain Connes
Also appears in collection : Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
This is joint work with A. Chamseddine and W. van Suijlekom. We compute the information theoretic von Neumann entropy of the state associated to the fermionic second quantization of a spectral triple. We show that this entropy is given by the spectral action of the spectral triple for a specific universal function. The main result is the surprising relation between this function and the Riemann zeta function.
