The Third Law of Quantum Thermodynamics in the Presence of Anomalous   Couplings
  The quantum thermodynamic functions of a harmonic oscillator coupled to a heat bath through velocity-dependent coupling are obtained analytically. It is shown that both the free energy and the entropy decay fast with the temperature in relation to that of the usual coupling from. This implies that the velocity-dependent coupling helps to ensure the third law of thermodynamics. 
Chun-Yang Wang, Jing-Dong Bao