Fully developed active turbulence defined through a non-equilibrium phase transition
Abstract
Non-equilibrium systems challenge the standard definitions of phases and phase transitions from equilibrium statistical physics. For example, in active fluids continuous energy injection at the microscale drives the system intrinsically out of equilibrium. This process gives rise to collective turbulent-like flows whose onset remains poorly defined. Here we show that the onset corresponds to an activity-driven phase transition, marked by the emergence of a system-spanning critical backbone of vorticity nodal lines. Combining two independent experiments, microtubule kinesin active nematics and dense suspensions of swimming bacteria, with large-scale simulations of active nematics and fluctuating nematohydrodynamics, we show that this transition occurs at a critical activity threshold. Below this threshold, vorticity structures are fragmented and vortex centres form only finite, mechanically floppy networks. Above this threshold, the nodal lines of the vorticity field percolate and the vortex centres form a rigid, system-spanning cluster. The geometric transition is characterised by the emergence of critical percolation statistics for the vorticity nodal lines, while the mechanical transition reflects the emergence of a vortex configuration that shows rigidity percolation statistics for vortex centres. We show that both transitions are absent in equilibrium systems that obey detailed balance, demonstrating that the transition is intrinsically non-equilibrium. These results establish an experimentally accessible definition of fully developed active turbulence, linking microscopic activity to macroscopic geometry, and mechanics of living systems.
Versions
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BibTeX
@misc{bonn2026fully,
title = {{Fully developed active turbulence defined through a non-equilibrium phase transition}},
author = {Lasse Bonn and Tianxiang Ma and Olga Bantysh and Wei Feng and Martin Cramer Pedersen and Guangyin Jing and Jordi Ignés-Mullol and Francesc Sagués and Nuno A. M. Araujo and Amin Doostmohammadi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39348},
eprint = {2609.39348},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39348},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fully developed active turbulence defined through a non-equilibrium phase transition
AU - Lasse Bonn
AU - Tianxiang Ma
AU - Olga Bantysh
AU - Wei Feng
AU - Martin Cramer Pedersen
AU - Guangyin Jing
AU - Jordi Ignés-Mullol
AU - Francesc Sagués
AU - Nuno A. M. Araujo
AU - Amin Doostmohammadi
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39348
UR - https://arxiv.org/abs/2609.39348
AB - Non-equilibrium systems challenge the standard definitions of phases and phase transitions from equilibrium statistical physics. For example, in active fluids continuous energy injection at the microscale drives the system intrinsically out of equilibrium. This process gives rise to collective turbulent-like flows whose onset remains poorly defined. Here we show that the onset corresponds to an activity-driven phase transition, marked by the emergence of a system-spanning critical backbone of vorticity nodal lines. Combining two independent experiments, microtubule kinesin active nematics and dense suspensions of swimming bacteria, with large-scale simulations of active nematics and fluctuating nematohydrodynamics, we show that this transition occurs at a critical activity threshold. Below this threshold, vorticity structures are fragmented and vortex centres form only finite, mechanically floppy networks. Above this threshold, the nodal lines of the vorticity field percolate and the vortex centres form a rigid, system-spanning cluster. The geometric transition is characterised by the emergence of critical percolation statistics for the vorticity nodal lines, while the mechanical transition reflects the emergence of a vortex configuration that shows rigidity percolation statistics for vortex centres. We show that both transitions are absent in equilibrium systems that obey detailed balance, demonstrating that the transition is intrinsically non-equilibrium. These results establish an experimentally accessible definition of fully developed active turbulence, linking microscopic activity to macroscopic geometry, and mechanics of living systems.
ER -