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

TL;DR

This work advances holographic understanding of non-equilibrium thermalization in a hot, dense, strongly coupled plasma by simulating homogeneous isotropization within the 2RCBH top-down Einstein–Maxwell–Dilaton framework and comparing to 1RCBH. By tracking non-equilibrium entropy via the apparent horizon, along with pressure anisotropy and scalar condensate, the authors uncover a universal entropy stairway of near-equilibrium plateaus whose timing is governed by the real part of the lowest QNM and whose decay is set by its imaginary part. A key finding is the emergence of purely imaginary QNMs at high R-charge density, which eventually dominate late-time dynamics and deform oscillatory relaxation, in particular for the pressure anisotropy. The results extend the known entropy–QNM connection to the 2RCBH model, quantify the staircase behavior, and provide quantitative tools for predicting late-time dynamics from QNM data, with implications for strongly coupled holographic fluids at finite chemical potential.

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.

Figures (8)

• Figure 1: Equation of state, scalar condensate, specific heat, and R-charge susceptibility for the 2RCBH and 1RCBH models.
• Figure 2: Comparison between the 2RCBH and 1RCBH models for different observables at $\mu/T=0$ considering IC1 in Table \ref{['tabICs']}. In Fig. \ref{['fig:ModelmuT0c']}, the gray shaded band demarcates the region where the DEC is violated, while the pink shaded band delimits the region where both the WEC and DEC are violated. In Fig. \ref{['fig:ModelmuT0f']} the parametrization of the support slopes is also shown for the entropy stairways.
• Figure 3: Comparison between the 2RCBH and 1RCBH models for different observables at $\mu/T=\pi/\sqrt{2}$ considering IC1 in Table \ref{['tabICs']}. In Fig. \ref{['fig:ModelmuT22c']}, the gray shaded band demarcates the region where the DEC is violated, while the pink shaded band delimits the region where both the WEC and DEC are violated. In Fig. \ref{['fig:ModelmuT22f']} the parametrization of the support slopes is also shown for the entropy stairways.
• Figure 4: Comparison for different observables evaluated at $\mu/T=4$, $\mu/T=5.065$, and $\mu/T=6$ in the case of the initial condition IC3 in Table \ref{['tabICs']} for the 2RCBH model. In Fig. \ref{['fig:muTIC3c']}, the gray shaded band demarcates the region where the DEC is violated, while the pink shaded band delimits the region where both the WEC and DEC are violated. In Fig. \ref{['fig:muTIC3f']} the parametrization of the support slopes is also shown for the entropy stairways.
• Figure 5: Comparison for different observables evaluated at $\mu/T=4$, $\mu/T=5.065$, and $\mu/T=6$ in the case of the initial condition IC4 in Table \ref{['tabICs']} for the 2RCBH model. In Fig. \ref{['fig:muTIC4c']}, the gray shaded band demarcates the region where the DEC is violated, while the pink shaded band delimits the region where both the WEC and DEC are violated. In Fig. \ref{['fig:muTIC4f']} the parametrization of the support slopes is also shown for the entropy stairways.