Can the correlated stability conjecture be saved?

TL;DR

This paper examines the validity of the correlated stability conjecture (CSC) for black branes, demonstrating that generalizations of thermodynamic stability do not necessarily imply dynamical stability, and presents a statistical model to illustrate this disconnect.

Contribution

It shows that extending the thermodynamic stability criterion does not save the correlated stability conjecture, and introduces a statistical model highlighting the lack of correlation.

Findings

Generalized thermodynamic stability criteria do not uphold CSC.

Thermodynamic and dynamical instabilities are generally uncorrelated.

A simple statistical model illustrates the disconnect between thermodynamic and dynamical stability.

Abstract

Correlated stability conjecture (CSC) proposed by Gubser and Mitra [1,2] linked the thermodynamic and classical (in)stabilities of black branes. In [3] it was shown that the thermodynamic instabilities, specifically the negative specific heat, indeed result in the instabilities in the hydrodynamic spectrum of holographically dual plasma excitations. Counter-examples of CSC were presented in the context of black branes with scalar hair undergoing a second-order phase transition [4,5]. The latter translationary invariant horizons have scalar hair, raising the question whether the asymptotic parameters of the scalar hair can be appropriately interpreted as additional charges leading to a generalization of the thermodynamic stability criterion. In this paper we show that the generalization of the thermodynamic stability criterion of this type can not save CSC. We further present a simple statistical model which makes it clear that thermodynamic and dynamical (in)stabilities generically are not correlated.