Fractional Entropy Decaying and the Third Law of Thermodynamics
  The quantum thermodynamic property of the fractional damping system is investigated extensively. A fractional power-law decaying entropy function is revealed which presents another evidence for the validity of the third law of thermodynamics in the quantum dissipative region. Several non-trivial characters are excavated such as that the entropy varies from a non-linear diverging function to a semi-linear decaying function of the fractional exponent as the temperature tends to absolute zero. 
Chun-Yang Wang, Xue-Mei Zong, Cui-Feng Sun, Hong Zhang, Zhen-Xue Song
cond-mat.stat-mech quant-ph