Reply on Comment on ``Extraction of work from a single thermal bath in   the quantum regime''
  In our recent letter [1] we discussed that thermodynamics is violated in quantum Brownian motion beyond the weak coupling limit. In his comment, Tasaki [2] derives an inequality for the relative entropy and claims, without making any dynamical assumption, that the Clausius inequality is valid, thus contradicting our statements [1]. Here we point out that the claim is unfunded, since the author did not properly identify the concept of heat. Tasaki also applies the inequality to Thomson's formulation of the second law. This application is invalid as well, since the author did not correctly identify the concept of work. Therefore, Tasaki's inequality is perfectly compatible with our findings. 
A.E. Allahverdyan, Th.M. Nieuwenhuizen