Basin Entropy in Boolean Network Ensembles

TL;DR

This paper introduces basin entropy as a new measure of information processing capacity in Boolean networks, showing it scales with system size only at criticality, indicating optimal information storage at phase boundaries.

Contribution

The paper proposes a novel measure called basin entropy to quantify information capacity in Boolean networks and analyzes its behavior across different regimes.

Findings

Basin entropy scales with system size at criticality.

Optimal information storage occurs at the boundary between order and disorder.

Critical regimes maximize the complexity of state space partitioning.

Abstract

The information processing capacity of a complex dynamical system is reflected in the partitioning of its state space into disjoint basins of attraction, with state trajectories in each basin flowing towards their corresponding attractor. We introduce a novel network parameter, the basin entropy, as a measure of the complexity of information that such a system is capable of storing. By studying ensembles of random Boolean networks, we find that the basin entropy scales with system size only in critical regimes, suggesting that the informationally optimal partition of the state space is achieved when the system is operating at the critical boundary between the ordered and disordered phases.