Illustration of the behaviour of the function defined in Eq. (55), for an active fraction ξ = 0.5, when averaged on 32 different realisations for particles numbers N ∈ {8, 12, 16, 24, 32, 48, 64 } × 10⁵. To compute , we binned the action-space domain (J_φ,J_r) = [ 0;2.5 ] × [ 0;0.2 ] in 100 × 50 regions. The values of have also been uniformly renormalised so as to clarify this representation. The dots corresponds to the snapshots of the simulations for which was computed, whereas the lines correspond to second-order fits. As expected, the smaller the number of particles, the noisier the simulation and the larger .