  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 [1,2]; in the high temperature limit we recover
the classical behavior.
