  As brown dwarfs and young giant planets cool down, they are known to
experience various chemical transitions --- for example from CO rich L-dwarfs
to methane rich T-dwarfs. Those chemical transitions are accompanied by
spectral transitions whose sharpness cannot be explained by chemistry alone. In
a series of articles, Tremblin et al. proposed that some of the yet unexplained
features associated to these transitions could be explained by a reduction of
the thermal gradient near the photosphere. To explain, in turn, this more
isothermal profile, they invoke the presence of an instability analogous to
fingering convection -- compositional convection -- triggered by the change in
mean molecular weight of the gas due to the chemical transitions mentioned
above. In this short note, we use existing arguments to demonstrate that any
turbulent transport, if present, would in fact increase the thermal gradient.
This misinterpretation comes from the fact that turbulence mixes/homogenizes
entropy (potential temperature) instead of temperature. So, while increasing
transport, turbulence in an initially stratified atmosphere actually carries
energy downward, whether it is due to fingering or any other type of
compositional convection. These processes therefore cannot explain the features
observed along the aforementioned transitions by reducing the thermal gradient
in the atmosphere of substellar objects. Understanding the microphysical and
dynamical properties of clouds at these transitions thus probably remains our
best way forward.
