Information transmission and criticality in the contact process

Abstract

In the present paper, we study the relation between criticality and information transmission in the one-dimensional contact process with infection parameter $\lambda .$ To do this we define the {\it sensitivity} of the process to its initial condition. This sensitivity increases for values of $\lambda <{\lambda }_c,$ the value of the critical parameter. The main point of the present paper is that we show that actually it continues increasing even after ${\lambda }_c$ and only starts decreasing for sufficiently large values of $\lambda .$ This provides a counterexample to the common belief that associates maximal information transmission to criticality.