This paper deals with the thermodynamic properties of a phantom field in a flat Friedmann-Robertson-Walker universe . General expressions for the temperature and entropy of a general dark-energy field with equation of state p = \omega \rho are derived from which we have deduced that , whereas the temperature of a cosmic phantom fluid ( \omega < -1 ) is definite negative , its entropy is always positive . We interpret that result in terms of the intrinsic quantum nature of the phantom field and apply it to ( i ) attain a consistent explanation for some recent results concerning the evolution of black holes which , induced by accreting phantom energy , gradually loss their mass to finally vanish exactly at the big rip , and ( ii ) introduce the concept of cosmological information and its relation with life and the anthropic principle . Some quantum statistical-thermodynamic properties of the quantum quantum field are also considered that include a generalized Wien law and the prediction of some novel phenomena such as the stimulated absorption of phantom energy and the anti-laser effect .