Cumulant dynamics in finite-memory diffusion

Abstract

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 (QGP) 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 multi-point Wigner functions and convert the freezeout correlators into acceptance-dependent cumulants along representative trajectories in the QCD phase diagram. While Fickian diffusion already causes the correlators to lag behind their instantaneous equilibrium values, finite current relaxation introduces an additional memory effect beyond this diffusive lag. As a result, current memory can suppress, shift, and reshape the non-monotonic behavior of the cumulants relative to both instantaneous equilibrium and Fickian diffusion, with the most visible effects appearing in higher-order cumulants and their ratios.