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  • Open Access

Thermodynamic efficiency of self-organization in nonequilibrium steady states

Qianyang Chen* and Mikhail Prokopenko

  • *Contact author: qianyang.chen@sydney.edu.au
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Phys. Rev. Research 8, 033265 – Published 3 September, 2026

DOI: https://doi.org/10.1103/zjjd-gr1b

Abstract

Active matter generates order or patterns through nonequilibrium dynamics. An open research challenge is to determine how efficiently a nonequilibrium self-organizing system can convert consumed energy into macroscopic order. We study an information-theoretic quantity that directly addresses this challenge by estimating the entropy reduction induced by a small control-parameter perturbation, relative to the generalized work required for the perturbation. This quantity has previously been considered mainly in an equilibrium or near-equilibrium context, and here we extend this framework and apply it to two nonequilibrium self-organizing systems: persistent and active Ising models. We observe that the thermodynamic efficiency of nonequilibrium systems maximizes at phase transitions, as in equilibrium systems. Furthermore, we compare thermodynamic efficiency and inferential efficiency across control parameters. While these two quantities are equal in equilibrium as a consequence of the fluctuation-dissipation theorem, we report that they diverge out of equilibrium, and the gap serves as a phenomenological signature of broken detailed balance.

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Phys. Rev. Research 8, 033265– Published 3 September, 2026
  • Received 7 May 2026
  • Accepted 18 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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