  The first law of thermodynamics at black hole horizons is known to be
obtainable from the gravitational field equations. A recent study claims that
the contributions at inner horizons should be considered in order to give the
conventional first law of black hole thermodynamics. Following this method, we
revisit the thermodynamic aspects of field equations in the Lovelock gravity
and f(R) gravity by focusing on two typical classes of charged black holes in
the two theories.
