  We analyze black hole thermodynamics in a generalized theory of gravity whose
Lagrangian is an arbitrary function of the metric, the Ricci tensor and a
scalar field. We can convert the theory into the Einstein frame via a
"Legendre" transformation or a conformal transformation. We calculate
thermodynamical variables both in the original frame and in the Einstein frame,
following the Iyer--Wald definition which satisfies the first law of
thermodynamics. We show that all thermodynamical variables defined in the
original frame are the same as those in the Einstein frame, if the spacetimes
in both frames are asymptotically flat, regular and possess event horizons with
non-zero temperatures. This result may be useful to study whether the second
law is still valid in the generalized theory of gravity.
