Invalidity of the Landauer inequality for information erasure in the   quantum regime
  A known aspect of the Clausius inequality is that an equilibrium system subjected to a squeezing $\d S<0$ of its entropy must release at least an amount $|\dbarrm Q|=T|\d S|$ of heat. This serves as a basis for the Landauer principle, which puts a lower bound $T\ln 2$ for the heat generated by erasure of one bit of information.   Here we show that in the world of quantum entanglement this law is broken, suggesting that quantum carriers of information can be more efficient than assumed so far. 
A.E. Allahverdyan and Th.M. Nieuwenhuizen