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 reorganization. We study the thermodynamic efficiency of interactions in self-organizing systems, which quantifies the change in the system’s order per unit of 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.
Highlights
Self-organization is defined as a spontaneous formation of spatial, temporal, and spatiotemporal structures or functions in a system comprising multiple interacting components
In the rest of this section, we focus on the behavior of η in the vicinity of the critical point, where it is possible to obtain an analytic solution for all thermodynamic quantities and study their scaling behavior
We modeled the thermodynamic efficiency of interactions in a canonical self-organizing system, by quantifying the change in the order in the system per unit of work done/extracted due to the changes in control parameters
Summary
Self-organization is defined as a spontaneous formation of spatial, temporal, and spatiotemporal structures or functions in a system comprising multiple interacting components. We study the thermodynamic efficiency of interactions within a canonical self-organizing system, aiming to clearly differentiate between phases of system dynamics, and identify the regimes when efficiency is maximal. The reasons for the maximal efficiency exhibited by systems during self-organization, i.e., at a critical regime, are articulated precisely in terms of the increased order (or the reduction of Shannon entropy) related to the amount of work carried out during the transition. This measure is defined for specific configurational changes (perturbations), rather than states or regimes—in line with the point made by Entropy 2021, 23, 757. We analytically evaluate dynamics of this model in the vicinity of a phase transition, prove that the thermodynamic efficiency has a power law divergence at the critical point, and compute its critical exponent
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