# Information transmission and criticality in the contact process

## TL;DR

This paper investigates how information transmission in the one-dimensional contact process varies with the infection parameter, revealing that maximum transmission occurs not at criticality but at other values, challenging common beliefs.

## Contribution

It demonstrates that information transmission, measured by sensitivity, continues to increase beyond the critical point, providing a counterexample to the idea that maximal information occurs at criticality.

## Key findings

- Sensitivity increases for λ < λ_c
- Sensitivity continues increasing after λ_c
- Maximum information transmission occurs away from criticality

## 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.