Equivalence of modified gravity equation to the Clausius relation

We explicitly show that the equations of motion for modified gravity theories of $F(R)$-gravity, the scalar-Gauss-Bonnet gravity, $F(\mathcal{G})$-gravity and the non-local gravity are equivalent to the Clausius relation in thermodynamics. In addition, we discuss the relation between the expression of the entropy and the contribution from the modified gravity as well as the matter to the definition of the energy flux (heat).Comment: 6 pages, no figure, several statements clarified, references adde

On thermodynamics second law in the modified Gauss Bonnet gravity

The second law and the generalized second law of thermodynamics in cosmology in the framework of the modified Gauss-Bonnet theory of gravity are investigated. The conditions upon which these laws hold are derived and discussed.Comment: 9pages, typos corrected, references adde

Radiative neutrino mass generation and dark energy

We study the models with radiative neutrino mass generation and explore the relation between the neutrino masses and dark energy. In these models, the pseudo-Nambu-Goldston bosons (pNGBs) arise at two-loop level via the Majorana neutrino masses. In particular, we demonstrate that the potential energy of the pNGB can be the dark energy potential and the observed value of the equation of state (EoS) parameter of the universe, $i.e.$, $w\simeq -1$, can be realized.Comment: 10 pages, 1 figure, a minor correction in Eq. (17