By generalizing the theory of convection to any type of thermal and compositional source terms (dia-batic processes), we show that thermohaline convection in Earth oceans, fingering convection in stellaratmospheres, and moist convection in Earth atmosphere are all deriving from the same general diabaticconvective instability. We show in particular that, when taking into account radiative heat transfer,radiative convection instability triggered by CO/CH$_4$ transition in the atmospheres of brown dwarfsis analog to moist convection and thermohaline convection. We derive a generalization of the mixinglength theory to include the effect of thermal and compositional source terms in 1D atmospheric codes.We show that CO/CH$_4$ radiative convection could significantly reduce the temperature gradient inthe atmospheres of brown dwarfs similarly to moist convection in Earth atmosphere thus possiblyexplaining the reddening in the spectrum of brown dwarfs. By using idealized two-dimensional hy-drodynamic simulations in the Ledoux unstable regime, we show that compositional source terms canindeed provoke a reduction of the temperature gradient in the atmosphere. The L/T transition couldbe explained by a bifurcation between the adiabatic and diabatic convective transports and could beseen as a giant cooling crisis an analog of the boiling crisis in two-phase convective flows.This mechanism generalized to other chemical transitions could be present in many giant and earth-likeexoplanets. The study of the impact of different parameters (e.g. effective temperature, compositionalchanges, etc) on CO/CH$_4$ radiative convection and the similarities and differencies with Earth moistconvection and thermohaline convection is also opening the possibility to use brown dwarfs as alaboratory to better understand some aspects of the physics at play in the climate of our own planet.