Homogeneous isotropization dynamics and entropy production in a hot and dense strongly interacting fluid

A bstract sWe numerically investigate the time evolution of the non-equilibrium entropy during the homogeneous isotropization dynamics of the 2 R-Charge Black Hole (2RCBH) model, corresponding to a top-down holographic fluid defined at finite temperature and R-charge density. In addition to the entropy production, we also analyze the time evolution of the pressure anisotropy and the scalar condensate of the medium. When the system is far-from-equilibrium the dominant and weak energy conditions can be transiently violated. For all initial conditions considered, we observe the emergence of a periodic sequence of several close plateaus forming a stairway for the entropy as the system approaches thermodynamic equilibrium. The entropy stairway allows for the entropy to encode a periodic structure without violating the second law of thermodynamics. In fact, the complex frequency of the lowest quasinormal mode (QNM) of the system is directly tied to the periodic structure of the entropy stairway, which provides another explicit numerical confirmation of a quite general connection between entropy production and QNMs previously discovered in the literature. Furthermore, when the chemical potential of the 2RCBH fluid exceeds a certain threshold, the pressure anisotropy exhibits a late-time decay governed by a purely imaginary QNM, and as the system is doped with increasing values of R-charge chemical potential the late-time equilibration pattern of the pressure anisotropy gets increasingly deformed, eventually losing the oscillatory behavior observed at lower values of chemical potential.