The second law of thermodynamics in the quantum Brownian oscillator at an arbitrary temperature

In the classical limit no work is needed to couple a system to a bath with sufficiently weak coupling strength (or with arbitrarily finite coupling strength for a linear system) at the same temperature. In the quantum domain this may be expected to change due to system-bath entanglement. Here we show analytically that the work needed to couple a single linear oscillator with finite strength to a bath cannot be less than the work obtainable from the oscillator when it decouples from the bath. Therefore, the quantum second law holds for an arbitrary temperature. This is a generalization of the previous results for zero temperature [Ford and O'Connell, Phys. Rev. Lett. 96, 020402 (2006); Kim and Mahler, Eur. Phys. J. B 54, 405 (2006)]; in the high temperature limit we recover the classical behavior. © 2007 EDP Sciences/ Società Italiana di Fisica/Springer-Verlag.