Statistical mechanics involving fractal temperature

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Khalili Golmankhaneh A.

Fractal and Fractional, cilt.3, sa.2, ss.1-12, 2019 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 3 Sayı: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3390/fractalfract3020020
  • Dergi Adı: Fractal and Fractional
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.1-12
  • Anahtar Kelimeler: Fractal Debye solid models, Fractal Einstein solid models, Fractal heat capacity, Local fractal calculus, Middle-τ Cantor sets
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.