  A known aspect of the Clausius inequality is that an equilibrium system
subjected to a squeezing $\d S$ 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. A quantum Brownian particle interacting with
its thermal bath can either generate less heat or even {\it adsorb} heat during
an analogous squeezing process, due to entanglement with the bath. The effect
exists even for weak but fixed coupling with the bath, provided that
temperature is low enough. This invalidates the Landauer bound in the quantum
regime, and suggests that quantum carriers of information can be much more
efficient than assumed so far.
