The third law of thermodynamics and the fractional entropies

Abstract

We consider the fractal calculus based Ubriaco and Machado entropies and investigate whether they conform to the third law of thermodynamics. The Ubriaco entropy satisfies the third law of thermodynamics in the interval 0<q≤1 exactly where it is also thermodynamically stable. The Machado entropy, on the other hand, yields diverging inverse temperature in the region 0<q≤1, albeit with non-vanishing negative entropy values. Therefore, despite the divergent inverse temperature behavior, the Machado entropy fails the third law of thermodynamics. We also show that the aforementioned results are also supported by the one-dimensional Ising model with no external field.