Dissipation enables robust extensive scaling of multipartite correlations

TL;DR

This paper explores how dissipation influences the scaling of multipartite correlations in stochastic networks, showing that robust extensive scaling requires nonequilibrium conditions and dissipation, unlike equilibrium systems.

Contribution

It demonstrates that dissipation enables robust extensive scaling of multipartite correlations in nonequilibrium systems, unlike equilibrium scenarios where such scaling is absent or fragile.

Findings

Multipartite correlations do not scale extensively at equilibrium.

Robust extensive scaling occurs only in nonequilibrium, time-dependent attractors.

Dissipation is essential for maintaining multipartite correlations.

Abstract

We investigate the multipartite mutual information between $N$ discrete-state stochastic units interacting in a network that is invariant under unit permutations. We show that when the system relaxes to fixed point attractors, multipartite correlations in the stationary state either do not scale extensively with $N$, or the extensive scaling is not robust to arbitrarily small perturbations of the system dynamics. In particular, robust extensive scaling cannot occur in thermodynamic equilibrium. In contrast, mutual information scales extensively when the system relaxes to time-dependent attractors (e.g., limit cycles), which can occur only far from equilibrium. This demonstrates the essential role of dissipation in the generation and maintenance of multipartite correlations. We illustrate our theory with the nonequilibrium Potts model.