Logical entropy of quantum dynamical systems

Ebrahimzadeh, Abolfazl

doi:10.1515/phys-2015-0058

Cited by 15 publications

(10 citation statements)

References 11 publications

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“…, p n ) ∈ n is a probability distribution, then the logical entropy of P is defined as the number h(P) = ∑ entropy, logical mutual information, logical cross entropy and logical divergence and their properties were also studied. In [21] Ebrahimzadeh defined and studied the notions of logical entropy of partitions and logical entropy of dynamical systems in quantum logics and in [22] the author introduced the notion of conditional logical entropy of dynamical systems on quantum logics. In the recently published paper [23], Markechová and Riečan deal with the study of logical entropy of fuzzy partitions and fuzzy dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

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Logical Entropy of Dynamical Systems—A General Model

2017

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Abstract:In the paper by Riečan and Markechová (Fuzzy Sets Syst. 96, 1998), some fuzzy modifications of Shannon's and Kolmogorov-Sinai's entropy were studied and the general scheme involving the presented models was introduced. Our aim in this contribution is to provide analogies of these results for the case of the logical entropy. We define the logical entropy and logical mutual information of finite partitions on the appropriate algebraic structure and prove basic properties of these measures. It is shown that, as a special case, we obtain the logical entropy of fuzzy partitions studied by Markechová and Riečan (Entropy 18, 2016). Finally, using the suggested concept of entropy of partitions we define the logical entropy of a dynamical system and prove that it is the same for two dynamical systems that are isomorphic.

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Section: Introductionmentioning

confidence: 99%

“…As a special case we obtain the logical entropy of fuzzy partitions introduced in [23]. It is noted that some investigations concerning entropy of dynamical systems and related notions in the above setup were conducted in [24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Logical Entropy of Dynamical Systems—A General Model

2017

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“…The logical entropy h L (U) is invariant under isomorphisms of dynamical systems; therefore, it can be used as an alternative tool for distinguishing some non-isomorphic dynamical systems. We note that some other recently published results concerning the logical entropy can be found, for example, in References [6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 72%

Tsallis Entropy of Fuzzy Dynamical Systems

Markechová

2018

Mathematics

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This article deals with the mathematical modeling of Tsallis entropy in fuzzy dynamical systems. At first, the concepts of Tsallis entropy and Tsallis conditional entropy of order where is a positive real number not equal to 1, of fuzzy partitions are introduced and their mathematical behavior is described. As an important result, we showed that the Tsallis entropy of fuzzy partitions of order satisfies the property of sub-additivity. This property permits the definition of the Tsallis entropy of order of a fuzzy dynamical system. It was shown that Tsallis entropy is an invariant under isomorphisms of fuzzy dynamical systems; thus, we acquired a tool for distinguishing some non-isomorphic fuzzy dynamical systems. Finally, we formulated a version of the Kolmogorov–Sinai theorem on generators for the case of the Tsallis entropy of a fuzzy dynamical system. The obtained results extend the results provided by Markechová and Riečan in Entropy, 2016, 18, 157, which are particularized to the case of logical entropy.

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“…It has been proven that the logical entropy H l (T) distinguishes non-isomorphic dynamical systems; so it can be used as an alternative instrument for distinguishing them. Note that some other recently published results regarding the logical entropy measure can be found, for example, in [9][10][11][12][13][14][15][16][17]. Actually, all of the above-mentioned studies are possible in the Kolmogorov probability theory based on the modern integration theory.…”

Section: Introductionmentioning

confidence: 99%

Logical entropy of dynamical systems in product MV-algebras and general scheme

Markechová

Riečan

2019

Adv Differ Equ

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The present paper is aimed at studying the entropy of dynamical systems in product MV-algebras. First, by using the concept of logical entropy of a partition in a product MV-algebra introduced and studied by Markechová et al. (Entropy 20:129, 2018), we define the logical entropy of a dynamical system in the studied algebraic structure. In addition, we introduce a general type of entropy of a product MV-algebra dynamical system that includes the logical entropy and the Kolmogorov-Sinai entropy as special cases. It is proved that the proposed entropy measure is invariant under isomorphism of product MV-algebra dynamical systems.

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Logical entropy of quantum dynamical systems

Cited by 15 publications

References 11 publications

Logical Entropy of Dynamical Systems—A General Model

Logical Entropy of Dynamical Systems—A General Model

Tsallis Entropy of Fuzzy Dynamical Systems

Logical entropy of dynamical systems in product MV-algebras and general scheme

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