  Let $X$ be a complex non-singular toric variety, $E$ an equivariant and ample
line bundle on $X$. We introduce a new functional $V_\infty$ on the set of
smooth, positive and invariant metrics on $E$. We compare $V_\infty$ to some
classical functionals. As an application, we study the variation of the
holomorphic analytic torsion.
