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Tsallis Entropy of Partitions in Quantum Logics

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Abstract

The purpose of the present paper is to study the Tsallis entropy Sq,t(P) of a partition P, and the Tsallis conditional entropy Sq,t(P|Q) of finite partitions P,Q in a quantum logic (L,t), where L is a quantum logic and t is a Bayessian state. We extend some results of Furuichi (J. Math. Phys. 47: 023302, 2006) to the partitions in (L,t). We study the concavity and subadditivity properties for Tsallis entropy of partitions in (L,t). We show that the subadditivity property in the case of q < 1 does not hold, in a true sense. It is proved that, for q > 1,Sq,t(P|Q) ≤ Sq,t(P), but in the case of \(q<1, S_{q,t} (P|Q) \nleq S_{q,t} (P)\), in general. We also study the chain rules for the information measures in (L,t); and present a numerical example to illustrate the results. We study Tsallis entropy and Tsallis conditional entropy of t-independent partitions. Finally, we show that, Tsallis entropy and Tsallis conditional entropy of partitions of a couple (L,t), are invariant under the relation of \(\circeq _{t}\).

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Authors and Affiliations

  1. Department of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran

    Abolfazl Ebrahimzadeh

  2. Department of Mathematics, Sirjan Branch, Islamic Azad University, Sirjan, Iran

    Zahra Eslami Giski

Authors
  1. Abolfazl Ebrahimzadeh
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  2. Zahra Eslami Giski
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Correspondence to Abolfazl Ebrahimzadeh.

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Ebrahimzadeh, A., Giski, Z.E. Tsallis Entropy of Partitions in Quantum Logics. Int J Theor Phys 58, 672–686 (2019). https://doi.org/10.1007/s10773-018-3966-1

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  • DOI: https://doi.org/10.1007/s10773-018-3966-1

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