Entropy and the spectral action

Understand

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 of our paper is the surprising relation between this function and the Riemann zeta function.
• It manifests itself in particular by the values of the coefficients $c(d)$ by which it multiplies the $d$ dimensional terms in the heat expansion of the spectral triple.