Hybrid thermalization in the large $N$ limit

TL;DR

This paper demonstrates that in large N gauge theories with semi-holography, the system can reach a unique global thermal equilibrium where both subsectors share the same temperature, with non-equilibrium states relaxing to this equilibrium.

Contribution

It completes the proof that a consistent global equilibrium state exists and is unique, and shows typical non-equilibrium states relax to this equilibrium at large energy densities.

Findings

Global equilibrium state is the maximum entropy state in the microcanonical ensemble.

Non-equilibrium states relax to the global equilibrium when energy density is high.

The equilibrium state is consistent with thermodynamics and statistical mechanics principles.

Abstract

Semi-holography provides a formulation of dynamics in gauge theories involving both weakly self-interacting (perturbative) and strongly self-interacting (non-perturbative) degrees of freedom. These two subsectors interact via their effective metrics and sources, while the full local energy-momentum tensor is conserved in the physical background metric. In the large $N$ limit, the subsectors have their individual entropy currents, and so the full system can reach a pseudo-equilibrium state in which each subsector has a different physical temperature. We first complete the proof that the global thermal equilibrium state, where both subsectors have the \textit{same} physical temperature, can be defined in consistency with the principles of thermodynamics and statistical mechanics. Particularly, we show that the global equilibrium state is the unique state with maximum entropy in the microcanonical ensemble. Furthermore, we show that in the large $N$ limit, a \textit{typical} non-equilibrium state of the full isolated system relaxes to the global equilibrium state when the average energy density is large compared to the scale set by the inter-system coupling. We discuss quantum statistical perspectives.