The time-fractional kinetic equation for the non-equilibrium processes

AYDINER E.

SCIENTIFIC REPORTS, cilt.11, sa.1, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1038/s41598-021-00135-7
  • Dergi Adı: SCIENTIFIC REPORTS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, BIOSIS, CAB Abstracts, Chemical Abstracts Core, EMBASE, MEDLINE, Veterinary Science Database, Directory of Open Access Journals
  • İstanbul Üniversitesi Adresli: Evet

Özet

In this study, we consider the non-Markovian dynamics of the generic non-equilibrium kinetic process. We summarize the generalized master equation, the continuous and discrete forms of the time-fractional diffusion equation. Using path integral formulation, we generalized the solutions of the Markovian system to the non-Markovian for the non-equilibrium kinetic processes. Then, we obtain the time-fractional kinetic equation for the non-equilibrium systems in terms of free energy. Finally, we introduce a time-fractional equation to analyse time evolution of the open probability for the deformed voltage-gated ion-channel system as an example.