  Although the entropy of black holes in any diffeomorphism invariant theory of
gravity can be expressed as the Wald entropy, the issue of whether the entropy
always obeys the second law of black hole thermodynamics remains open. Since
the nonminimal coupling interaction between gravity and the electromagnetic
field in the general quadric corrected Einstein-Maxwell gravity can
sufficiently influence the expression of the Wald entropy, we check whether the
Wald entropy of black holes in the quadric corrected gravity still satisfies
the second law. A quasistationary accreting process of black holes is first
considered, which describes that black holes are perturbed by matter fields and
eventually settle down to a stationary state. Two assumptions that the matter
fields should obey the null energy condition and that a regular bifurcation
surface exists on the background spacetime are further proposed. According to
the two assumptions and the Raychaudhuri equation, we demonstrate that the Wald
entropy monotonically increases along the future event horizon under the linear
order approximation of the perturbation. This result indicates that the Wald
entropy of black holes in the quadric corrected gravity strictly obeys the
linearized second law of thermodynamics.
