  We consider a quantum harmonic oscillator linearly coupled to a bath of
harmonic oscillators and evaluate the degree of entanglement between system and
bath using the negativity as an exact entanglement measure. We establish the
existence of a critical temperature above which the system-bath negativity
vanishes. Our results imply that system-bath entanglement is not responsible
for the violation of the Clausius inequality observed in the low
temperature/strong coupling regime [Phys. Rev. Lett. 85, 1799 (2000)], as the
latter still occurs well above the critical temperature.
