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 λ. We introduce a notion of sensitivity of the process to its initial condition and prove that it increases not only for values of λ< λ_c, the value of the critical parameter, but keeps increasing even after λ_c, before finally starting to decrease for values of λ sufficiently above λ_c. This provides a counterexample to the common belief that associates maximal information transmission to criticality.