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.

Topics: Quantum Physics, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1401.1425

We use derivatives to prove the equivalences between MacWilliams identity and its four equivalent forms, and present new interpretations for the four equivalent forms. Our results explicitly give out the relationships between MacWilliams identity and its four equivalent forms.

Topics: Mathematics, Computing Research Repository, Information Theory

Source: http://arxiv.org/abs/1401.3582