Can Sobolev inequality be written for Sharma-Mittal entropy?

O. Üzengi Aktürk, E. Aktürk, M. Tomak

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

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 Pösch-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.

Original languageEnglish
Pages (from-to)3310-3320
Number of pages11
JournalInternational Journal of Theoretical Physics
Volume47
Issue number12
DOIs
StatePublished - Dec 2008
Externally publishedYes

Keywords

  • Renyi entropy
  • Shannon entropy
  • Sharma-Mittal entropy
  • Sobolev inequality
  • Tsallis entropy

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