  We seek an analogy of the mathematical form of the alternative form of
Einstein's field equations for Lovelock's field equations. We find that the
price for this analogy is to accept the existence of the trace anomaly of the
energy-momentum tensor even in classical treatments. As an example, we take
this analogy to any generic second order Lagrangian and exactly derive the
trace anomaly relation suggested by Duff. This indicates that an intrinsic
reason for the existence of such a relation should perhaps be, classically,
somehow related to the covariance of the form of Einstein's equations.
