  We analyze the interaction between Dark Energy and Dark Matter from a
thermodynamical perspective. By assuming they have different temperatures, we
study the possibility of occurring a decay from Dark Matter into Dark Energy,
characterized by a negative parameter $Q$. We find that, if at least one of the
fluids has non vanishing chemical potential, for instance $\mu_x<0$ and
$\mu_{dm}=0$ or $\mu_x=0$ and $\mu_{dm}>0$, the decay is possible, where
$\mu_x$ and $\mu_{dm}$ are the chemical potentials of Dark Energy and Dark
Matter, respectively. Using recent cosmological data, we find that, for a
fairly simple interaction, the Dark Matter decay is favored with a probability
of $\sim 93%$ over the Dark Energy decay. This result comes from a likelihood
analysis where only background evolution has been considered.
