  We prove the generalized second law (GSL) for higher curvature gravity
theories when the matter sector is non-minimally coupled. The validity of our
proof is in the regime of linearized fluctuations about equilibrium black
holes, which is the same regime as considered in the previous proofs by Wall
and Sarkar. These proofs were provided in different gravity theories - for
instance, Lovelock theory and higher curvature gravity - but the matter sector
was always taken to be minimally coupled. In this article, we describe how to
generalize the proof of linearized semi-classical GSL when the matter sector
comes with non-minimal couplings. The proof proceeds by suitably evaluating the
matter path integral in the stress tensor expectation value by treating the
higher derivative couplings in an effective field theory setting. We use the
recently established result of the linearized second law for such theories.
