  The main purpose of this note is to construct two functionals of the positive
solutions to the conjugate heat equation associated to the metrics evolving by
the conformal Ricci flow on closed manifolds. We show that they are
nondecreasing by calculating the explicit evolution formulas of these
functionals. For the entropy functional we give another proof of the
monotonicity by establishing a pointwise formula. Moreover, we show that the
increase are strict unless the metrics are Einstein.
