Can Sobolev Inequality Be Written for Sharma-Mittal Entropy?

Akturk O. U., Akturk E., TOMAK M.

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, cilt.47, sa.12, ss.3310-3320, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 12
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1007/s10773-008-9766-2
  • Dergi Adı: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3310-3320
  • Anahtar Kelimeler: Sharma-Mittal entropy, Sobolev inequality, Tsallis entropy, Renyi entropy, Shannon entropy, FOKKER-PLANCK EQUATIONS, BOLTZMANN-GIBBS STATISTICS, RENYI ENTROPIES, GENERALIZED THERMOSTATISTICS, UNCERTAINTY RELATION, HARMONIC-OSCILLATOR, FRACTAL APPROACH, ISING CHAIN, TSALLIS, QUANTUM
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we focus on Sobolev inequality in the context of Sharma-Mittal entropy. Using this new inequality, generalized entropic uncertainty relation in accordance with Sharma-Mittal entropy is derived and the pseudoadditivity relation has been obtained. This new entropic uncertainty relation has then been applied to physical examples such as one dimensional harmonic oscillator and Posch-Teller potential. Finally, it has been shown that for certain values of the parameters of Sharma-Mittal measure, the present results reduce to the corresponding results of Shannon, Renyi and Tsallis measures.