  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 and the correlation function is
absolutely integrable. 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. 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.
Finally, we discuss a ``paradox'' raising by the negative susceptibility in
holography and its resolution.
