System-bath entanglement in quantum thermodynamics

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.