Thermodynamic efficiency of interactions in self-organizing systems

TL;DR

This paper introduces a thermodynamic efficiency measure for self-organizing systems, showing it diverges at critical points, thus formalizing how order emerges in complex systems across various domains.

Contribution

It defines and analytically derives a thermodynamic efficiency measure for self-organizing systems, demonstrating divergence at criticality in the Curie-Weiss Ising model.

Findings

Efficiency diverges at the critical point of phase transition.

Efficiency analysis applies to both external field and coupling strength variations.

Formalizes thermodynamic efficiency in diverse self-organizing systems.

Abstract

The emergence of global order in complex systems with locally interacting components is most striking at criticality, where small changes in control parameters result in a sudden global re-organization. We introduce a measure of thermodynamic efficiency of interactions in self-organizing systems, which quantifies the change in the system's order per unit work carried out on (or extracted from) the system. We analytically derive the thermodynamic efficiency of interactions for the case of quasi-static variations of control parameters in the exactly solvable Curie-Weiss (fully connected) Ising model, and demonstrate that this quantity diverges at the critical point of a second order phase transition. This divergence is shown for quasi-static perturbations in both control parameters, the external field and the coupling strength. Our analysis formalizes an intuitive understanding of thermodynamic efficiency across diverse self-organizing dynamics in physical, biological and social domains.