Supersymmetric multiplex networks described by coupled Bose and Fermi statistics

TL;DR

This paper introduces supersymmetric multiplex networks modeled by coupled Bose and Fermi statistics, revealing their complex structure, phase transitions, and quantum information properties, bridging classical dynamics and quantum entanglement.

Contribution

It presents a novel framework linking supersymmetric multiplex network growth with quantum statistical mechanics and extends quantum information measures to network layers.

Findings

Layers can undergo Bose-Einstein condensation.

A simple relation between entanglement entropy and entropy rate is established.

Supersymmetric multiplex networks exhibit unique symmetry properties.

Abstract

Until now, no simple symmetries have been detected in complex networks. Here we show that, in growing multiplex networks the symmetries of multilayer structures can be exploited by their dynamical rules, forming supersymmetric multiplex networks described by coupled Bose-Einstein and Fermi-Dirac quantum statistics. The supersymmetric multiplex is formed by layers which are scale-free networks and can display a Bose-Einstein condensation of the links. To characterize the complexity of the supersymmetric multiplex using quantum information tools, we extend the definition of the network entanglement entropy to the layers of multiplex networks. Interestingly we observe a very simple relation between the entanglement entropies of the layers of the supersymmetric multiplex network and the entropy rate of the same multiplex network. This relation therefore connects the classical non equilibrium growing dynamics of the supersymmetric multiplex network with its quantum information static characteristics.