Onsager Condensation in Chiral Active Matter: Universality of Supersonic Topological Gas Dynamics

TL;DR

This work addresses how dissipative active turbulence in overdamped chiral matter can exhibit inertial-like transport through a universal topological mechanism. By modeling a large ensemble of phase-coupled agents and introducing a renormalised fluid element, the authors establish a hydrodynamic limit isomorphic to shallow-water theory, with an emergent negative-temperature Onsager dipole that acts as a dynamic attractor via a topological heat pump. Key results show a scale-dependent spectral dichotomy: a microscopic $E(k)\sim k^{-3}$ arising from defect enstrophy, and a macroscopic inertial cascade $E_{\text{RFE}}(k)\sim k^{-5/3}$ revealed after renormalisation, along with a negative spectral flux $\Pi(k)<0$ indicating an inverse cascade toward the system size. The findings unify active swarms with classical inviscid fluids, provide a mechanism for robust large-scale transport in overdamped systems, and point toward broad implications for biology, robotics, and microfluidics where disorder can seed coherent, supersonic topological dynamics.

Abstract

To explain how dissipative active turbulence sustains inertial cascades, we map overdamped chiral flocks to a compressible vortex gas, realizing supersonic topological gas dynamics. Here, Mach cones function as acoustic horizons, shielding defect cores from the radiative decay of shallow water flows. Disorder activates a topological heat pump driving an inverse cascade toward a negative-temperature Onsager dipole, unless arrested into a vortex glass. This identifies a universality class unifying active swarms with classical inviscid fluids.

Figures (8)

• Figure 1: The emergence of the Onsager dipole in simulated chiral active matter, shown in seven temporal snapshots of the simulation space. The top row shows the raw particle point-clouds, with black denoting 'trapped' (superconducting) agents and red denoting 'running' (phase slipping) agents ivarsen_information_2025, the middle row shows topological charge $m$, and the bottom row shows inertial mass $R^2$ (with flow lines overlaid), using the colorscales indicated.
• Figure 2: Energy characteristics of the simulation run in Figure \ref{['fig:0']}. Panel a) shows the defect (phase singularity) count, with a $t^{-0.75}$ powerlaw scaling carnevale_evolution_1991 shown with a dashed, green line. Panel b) shows the spectral flux (Eq. \ref{['eq:spectralflux']}) for the RFE (blue, left $y$-axis) and raw (red, right $y$-axis) fields, taking the median of the entire simulation. Panel c) shows the energy spectrum $E(k)$ for the RFE (blue) and raw (red) fields; a spectral scaling of $k^{-5/3}$ and $k^{-8/3}\approx k^{-2.67}$ is indicated with dotted and solid green lines respectively, and $k_c$ is indicated with a dashed, grey line, as in Panel b). Panel d) shows the thermodynamic trajectory, plotting order versus coarse-grained kinetic energy for the simulation evolution.
• Figure 3: Active vortex glass made of particles whose raw distribution features an inverse cascade ($\Pi(k)<0$), but whose RFE field features a forward-cascade ($\Pi(k)>0$). The defect count falls off drastically and flattens; defect merger is arrested and the ensemble settles in a frozen defect lattice. Top row shows the RFE particle point-cloud while bottom row shows topological charge, while the columns correspond to seven temporal snapshots.
• Figure 4: The three distributions in $\Delta \omega$ corresponding to the three thermodynamic phases in Table \ref{['tab:phase_diagram']}, showing only the positive component ($\omega_i$ is symmetric around 0). The lower limit on the $x$-axis is given by $(2\Lambda)^{-1}$, the hypothetical "box-size fluctuation.".
• Figure 5: Summary of a Phase I simulation.. RFE particles as point-clouds (top row) and topological charge (bottom row) mapped with a colorscale; timestamps are indicated.