  We introduce a Riemannian metric on certain hyperbolic components in the
moduli space of degree $d \ge 2$ polynomials. Our metric is constructed by
considering the measure-theoretic entropy of a polynomial with respect to some
equilibrium state. As applications, we show that the Hausdorff dimension
function has no local maximum on such hyperbolic components. We also give a
sufficient condition for a point not being a critical point of the Hausdorff
dimension function.
