Statistical Mechanics Involving Fractal Temperature

Abstract

In this paper, the Schrödinger equation involving a fractal time derivative is solved and corresponding eigenvalues and eigenfunctions are given. A partition function for fractal eigenvalues is defined. For generalizing thermodynamics, fractal temperature is considered, and adapted equations are defined. As an application, we present fractal Dulong-Petit, Debye, and Einstein solid models and corresponding fractal heat capacity. Furthermore, the density of states for fractal spaces with fractional dimension is obtained. Graphs and examples are given to show details.

Keywords

• local fractal calculus
• middle-<i>τ</i> Cantor sets
• fractal Einstein solid models
• fractal Debye solid models
• fractal heat capacity