  This paper starts from a toy model for inflation in a class of modified
theories of gravity in the metric formalism. Instead of the standard procedure
-- assuming a non-linear Lagrangian $f(R)$ in the Jordan frame -- we start from
a simple $\phi^2$ potential in the Einstein frame and investigate the
corresponding $f(R)$ in the former picture. The addition of an ad-hoc
Cosmological Constant in the Einstein frame leads to a Thermodynamical
interpretation of this physical system, which allows further insight on its
(meta)stability and evolution.
