For a strongly coupled system that has a gravity dual description, we show that the standard holographic dictionary yields a nonnegative susceptibility when the system is in thermodynamic equilibrium.  When the system has no spontaneous condensation or has a spontaneous $\mathbb{Z}_2$-symmetry breaking, we find that the ``trace energy condition'' is violated in many cases (see Eq.~\eqref{tracebk}). There is a normalized grand potential density that is monotonic as accessing to lower scales, providing a candidate $c$-function characterizing the number of effective degrees of freedom.  Moreover, we find that  some extensively discussed  holography models in the literature are not consistent with holography due to negative susceptibility. 

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Contact联系人  王少江