Information Transmission and Criticality in the Contact Process

In the present paper, we study the relation between criticality and information transmission in the one-dimensional contact process with infection parameter \(\lambda .\) We introduce a notion of sensitivity of the process to its initial condition and prove that it increases not only for values of \(\lambda < \lambda _c, \) the value of the critical parameter, but keeps increasing even after \( \lambda _c , \) before finally starting to decrease for values of \(\lambda \) sufficiently above \(\lambda _c.\) This provides a counterexample to the common belief that associates maximal information transmission to criticality.