Abstract
We extend Padmanabhan's entropy functional formalism to show that, in addition to the Gauss–Bonnet (GB) or the entire series of Lanczos–Lovelock Lagrangians already obtained, more general higher-order corrections to General Relativity, i.e. the so-called modified gravity theories, also emerge naturally from this formalism. This extension shows that the formalism constitutes a valuable tool to investigate, at each order in the curvature, the possible structure the higher-order modified gravity theories might have. As an application, the extended formalism is used to evaluate the horizon entropy in a modified gravity theory of the second-order in the curvature. Our findings are in agreement with previous results from the literature.
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