  In this work, we derive an upper bound on energetic quantities, namely vacuum
energy and free energy, for static solutions of Einstein-Scalar theory in four
dimensional asymptotically locally Anti-de Sitter(AlAdS) spacetime with a
nontrivial scalar potential where the scalar field mass parameter($m^2$) is
equal to 0 or -2. This system is the holographic dual of strongly coupled
conformal field theory(CFT) in three dimensions being deformed by a relevant or
marginal scalar operator of conformal dimension $\Delta=1, 2, 3$. The bound is
derived from a purely gravitational perspective regardless of the inhomogeneity
of the static conformal boundary of AlAdS and the source of the deformation. We
demonstrate the bound in simple settings and check the consistency with the
known previous bounds.
