Appears in collections : Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette, Fields medallists - 1982

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.