Thermodynamic efficiency of interactions in self-organizing systems

Ramil Nigmatullin*, Mikhail Prokopenko

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)
    6 Downloads (Pure)


    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.

    Original languageEnglish
    Article number757
    Pages (from-to)1-12
    Number of pages12
    Issue number6
    Publication statusPublished - Jun 2021

    Bibliographical note

    © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


    • Phase transitions
    • Self-organized systems
    • Thermodynamics


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