# The behaviour of information flow near criticality

## TL;DR

This study uses stochastic simulations of a 2D Ising model to analyze how information transmission varies near criticality, revealing optimal conditions for information flow depending on temperature and input dynamics.

## Contribution

It provides new insights into how information transmission depends on system parameters near criticality using detailed stochastic simulations.

## Key findings

- Mutual information varies non-monotonically with temperature.
- Maximum information transmission rate occurs at an optimal input correlation time.
- Optimal temperature for information transfer is above the critical point and shifts with distance.

## Abstract

Recent experiments have indicated that many biological systems self-organise near their critical point, which hints at a common design principle. While it has been suggested that information transmission is optimized near the critical point, it remains unclear how information transmission depends on the dynamics of the input signal, the distance over which the information needs to be transmitted, and the distance to the critical point. Here we employ stochastic simulations of a driven 2D Ising system and study the instantaneous mutual information and the information transmission rate between a driven input spin and an output spin. The instantaneous mutual information varies non-monotonically with the temperature, but increases monotonically with the correlation time of the input signal. In contrast, the information transmission rate exhibits a maximum as a function of the input correlation time. Moreover, there exists an optimal temperature that maximizes this maximum information transmission rate. It arises from a tradeoff between the necessity to respond fast to changes in the input so that more information per unit amount of time can be transmitted, and the need to respond to reliably. The optimal temperature lies above the critical point, but moves towards it as the distance between the input and output spin is increased.