  We study the generic transport of slice energy between the scalar field
generated by the conformal transformation of higher-order gravity theories and
the matter component. We give precise relations for this exchange in the cases
of dust and perfect fluids. We show that, unless we are in a stationary
spacetime where slice energy is always conserved, in non-stationary situations
contributions to the total slice energy depend on whether or not test matter
follows geodesics in both frame representations of the dynamics, that is on
whether or not the two conformally related frames are physically
indistinguishable.
