Fluctuations of the elliptic flow v₂ in heavy-ion collisions are usually explained as a linear response to the initial anisotropy ε₂, with a small cubic correction. Now, an analysis based on event-by-event hydrodynamic simulations reveals significant deviations from this scheme. The authors decompose the response order by order in the cumulant expansion of the ε₂ and v₂ fluctuations, working in the intrinsic frame where the magnitude and direction of the impact parameter are fixed.

The results show two unexpected effects. On the one hand, the asymmetry of the v₂ fluctuations turns out to be opposite to that of the ε₂ fluctuations. On the other, the response to ε₂ fluctuations is approximately 10-20% larger than the response to the average geometry. This second effect is not explained by the cubic response and increases the splitting between the cumulants v₂{2} and v₂{4}, two observables measured with precision in Pb+Pb collisions at the LHC.

Collective flow is the most prominent signature of the hydrodynamic evolution of the quark-gluon plasma created at the LHC, and its event-by-event fluctuations encode information about the early stages of the collision. Understanding precisely the relation between the initial geometry and the final flow is essential to extract properties of the medium, such as its viscosity, from the data. The described deviation suggests that the framework of linear response plus cubic correction is not sufficient to describe the full range of observed fluctuations.

The work paves the way to refine the hydrodynamic models and analysis chains used to interpret flow measurements at the LHC. If the effect is confirmed, it could affect the determination of quark-gluon plasma parameters and the comparison between theory and data from ATLAS, CMS and ALICE.