Stairway to equilibrium entropy

We compute the time evolution of the nonequilibrium entropy in the homogeneous isotropization dynamics of the 1 R-Charge Black Hole model, which has a critical point in its conformal phase diagram defined at finite temperature and R-charge density. We also evaluate the time evolution of the pressure anisotropy and the scalar condensate of the medium. We disclose a new feature (not present in the Bjorken flow dynamics analyzed in previous works), which is observed for all the analyzed initial data: the formation of a periodic sequence of several close plateaus in the form of a stairway for the entropy density near thermodynamic equilibrium. We find that the period of plateau formation in the stairway is half the period of oscillations of the slowest quasinormal mode of the system, which is therefore strongly tied to the late-time dissipative dynamics of the system associated with the irreversibility of entropy production. For the particular case of the purely thermal Supersymmetric Yang-Mills plasma at zero density and vanishing scalar condensate, we find that the period of the stairway is half the period of oscillations of the slowest quasinormal mode associated with the late-time equilibration of the pressure anisotropy of the fluid, while at finite chemical potential the slowest quasinormal mode of the system is associated with the late-time equilibration of the scalar condensate.