  We investigate the first law of thermodynamics and entropy associated to the
apparent horizon of (non-flat) FLRW space-time in different theories of
modified gravity and in the presence of a perfect fluid of matter. We pose our
attention on those theories which lead to second order differential field
equations on FLRW background. In this way, we observe that one may obtain a
formula for entropy in terms of the radius of the apparent horizon only. Thus,
when considering a modification to the area law of General Relativity, it is
possible to reconstruct the gravitational lagrangian consistent with the
corresponding first law.

General Relativity and Quantum Cosmology