Fractional entropy decay and the third law of thermodynamics

We report in this paper a theoretical study on the quantum thermodynamic properties of a fractional damping system. Through the analysis, few nontrivial characteristics are revealed, which include (1) a fractional power-law decay entropy function, which provides an evidence for the validity of the third law of thermodynamics in the quantum dissipative region and (2) the varying of the entropy from a nonlinear divergent function to a semilinear decay function with a fractional exponent as the temperature approaches absolute zero.

Figure 1

Free energy and entropy of the FD system as a function of the inverse temperature. Dimensionless parameters in use are ${\eta }_{\alpha }=\hslash {\omega }_{{}_0}=k_B=1.0$.

Figure 2

Entropy of the FD system plotted as a function of the fractional exponent at various system temperatures. Inserts: local amplification of the linear curves. Dimensionless units are used as those of Fig. 1.