Fractional Variational Principle in Macroscopic Picture

Abstract

Using fractional integrals properties, a thermodynamical fractional variational principle δ(Dω(-1-1/k)ρ(ω)) = 0 is deduced. The fractal character is due to the non-differentiable nature of the microscopic level. Our results show that statistical thermodynamics is a variational theory. In this respect, another definition of the entropy is introduced.