Log-normal Superstatistics Reveals Statistical Resilience in the Panic Response of Confined Ants

Abstract

We report the emergence of Log-normal Superstatistics in the collective motion of ants confined in a quasi-2D arena and exposed to a panic-inducing stimulus. A data-driven superstatistical Langevin model accurately reproduces the transition from stationary behavior to an organized escape response, characterized by non-Gaussian velocity distributions and a stochastic diffusion coefficient. Our findings show that danger information propagates via a memory-limited, cascade-like mechanism, resulting in a stable cluster formation despite individual memory constraints. These results indicate that a slowly varying diffusivity arises from the multiplicative combination of interaction-mediated processes under confinement, leading naturally to Log-normal fluctuations. The persistence of this statistical structure under panic reveals a form of collective resilience, establishing a mechanistic bridge between Superstatistics and living active matter in confined environments.

Figures (8)

• Figure 1: Experimental Setup and Collective Escape Response. (a) Experimental setup and snapshots of experiments for (b) Thin and (c) Ctrl protocols with the center of mass (CM) trajectory colored by 5-minute intervals (green, blue, red). (d) Net horizontal CM displacement relative to its initial position for the Thin protocol, as predicted by the superstatistical model in Eq. \ref{['eq:panic-langevin-model']} (SSModel); (e) corresponding experimental data for the Ctrl protocol.
• Figure 2: Speed-Dependent Fluctuations and Time-Scale Separation in the Baseline Regime. (a) Mean (blue/orange) and fluctuation intensity (dark/light green) of parallel and perpendicular acceleration components vs. speed. Error bars account for the standard error of the mean. Parallel acceleration scales linearly, perpendicular remains near zero, and both speed-dependent standard deviations fit Eq. \ref{['eq:sigma-in-v']}. Note that $\mu(v)$ and $\sigma(v)$ differ in units (i.e., $\mathrm{cm \, s}^{-2}$ and $\mathrm{cm \, s}^{-3/2}$, respectively). (b) Autocorrelation function of acceleration fluctuations around their mean (Noise Autocorrelation Function, NACF). Parallel and perpendicular components are shown in blue and orange, respectively. The fluctuations exhibit no temporal correlation, indicating uncorrelated noise. (c) Probability density function (PDF) of parallel and perpendicular acceleration fluctuations. The non-Gaussian shape is accurately captured by the SSModel (Eq. \ref{['eq:ss-model']}), which combines a Log-normal and Gaussian dynamics, but it cannot be explained only by Gaussian noise (G. Noise) with the state-dependent intensity $\sigma(v)$. (d) Time-average of local flatness of Cartesian velocity components (Eq. \ref{['eq:flatness']}). The dashed line marks the Gaussian value. Inset: typical realization of $D(t)$ (dark red) varies more slowly than $v_x(t)$ (dark blue) over $\sim 50 \,\mathrm{s}$.
• Figure 3: Log-normal Diffusivity and Non-Gaussian Velocities in the Baseline Regime. (a) Probability density (PDF) of diffusion coefficient $D$ (standardized) fitted to a Log-normal distribution. Inset shows the tail up to 15 standard deviations. (b) Velocity PDF with Gaussian, Laplace, and power-law (Lévy stable) fits. The SSModel \ref{['eq:ss-model']} (solid line) captures the central peak and tails beyond Gaussian decay.
• Figure 4: Temporal Signatures of Panic and Cluster Stabilization in the Panic Regime. (a) Time evolution of the parameters in Eq. \ref{['eq:sigma-in-v']}, obtained from independent fits in successive panic-regime time windows. $\Delta\Sigma(t)$ and $v_\sigma(t)$ show a sharp change at minute 9.2, while $\Sigma(t)$ remains stable. (b) Probability of finding an ant from the safe cell at a distance less than or equal to $2 \,\mathrm{cm}$ from the barrier. The last 5 minutes of the experiment are highlighted in orange, where the curve remains approximately constant near zero. During this interval, the ant cluster is stable.
• Figure 5: Boundary Effects and Effective Wall Thickness. (a) Cartesian acceleration components as functions of Cartesian position, with error bars showing the standard error of the mean. Inset: acceleration absolute value as a function of the distance from the walls. A characteristic length $\ell_w=0.6\,\mathrm{cm}$ is defined as the effective wall thickness. (b) The grey sections have been removed from a sample trajectory, as they are within a distance $\ell_w$ from the walls: in order to ensure that statistics is not contaminated by boundary effects, we only use for analysis the non-gray sections.