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

TL;DR

This study numerically explores the entropy evolution and isotropization in a holographic strongly interacting fluid, revealing a stairway pattern in entropy and linking it to quasinormal modes, with effects of chemical potential on pressure anisotropy.

Contribution

It introduces a detailed numerical analysis of entropy production and pressure anisotropy in a holographic model, highlighting the connection to quasinormal modes and effects of R-charge chemical potential.

Findings

Entropy exhibits a stairway pattern during isotropization.

The lowest quasinormal mode frequency relates to the entropy structure.

High chemical potential alters pressure anisotropy decay, suppressing oscillations.

Abstract

We 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.