Cumulant dynamics in finite-memory diffusion

Fluctuations of conserved charges are among the main proposed signatures of the quantum chromodynamics (QCD) critical point, but their interpretation requires a dynamical description of how fluctuation correlators evolve during the finite lifetime of the quark-gluon plasma fireball. The standard baseline for this evolution is Fickian diffusion, in which the diffusive current follows the local density gradient instantaneously. This instantaneous-current limit can miss delayed-response effects when the current-relaxation time becomes comparable to the relaxation time of the relevant fluctuation modes. In this work we extend this baseline to Maxwell-Cattaneo diffusion, where the current relaxes on a finite time scale and therefore retains memory. We derive closed evolution equations for multipoint Wigner functions and convert the freeze-out correlators into acceptance-dependent cumulants along representative trajectories in the QCD phase diagram. While Fickian diffusion already causes the