  We compute the time evolution of the non-equilibrium entropy in the
homogeneous isotropization dynamics of the 1RCBH 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 to the irreversibility of entropy production.
For the particular case of the purely thermal SYM 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 to 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 to the late time equilibration of the scalar condensate.
