  We present an analytical model for the evolution of brown dwarfs in quadratic
Palatini f(R) gravity. We improve previous studies by adopting a more realistic
description of the partially-degenerate state that characterizes brown dwarfs.
Furthermore, we take into account the hydrogen metallic-molecular phase
transition between the interior of the brown dwarf and its photosphere. For
such improved model, we revise the cooling process of sub-stellar objects.
