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.
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