Preprint Article Version 1 This version is not peer-reviewed

Application of the Shannon Entropy in the Construction of a Paraconsistent Model of the Atom

Version 1 : Received: 20 November 2019 / Approved: 21 November 2019 / Online: 21 November 2019 (10:41:58 CET)
Version 2 : Received: 20 February 2020 / Approved: 24 February 2020 / Online: 24 February 2020 (04:04:11 CET)

How to cite: da Silva Filho, J.I. Application of the Shannon Entropy in the Construction of a Paraconsistent Model of the Atom. Preprints 2019, 2019110250 (doi: 10.20944/preprints201911.0250.v1). da Silva Filho, J.I. Application of the Shannon Entropy in the Construction of a Paraconsistent Model of the Atom. Preprints 2019, 2019110250 (doi: 10.20944/preprints201911.0250.v1).

Abstract

In this work, we present a model of the atom that is based on nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The model proposed in this work is constructed with the extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v) that is associated with an interlaced bilattice of four vertices. We used the logarithmic function of the Shannon entropy H(s) with the inclusion of the normalized Planck constant ħ to construct the paraconsistent equations. Through the analyses of the interlaced bilattice, comparative values are obtained for some of the phenomena and effects of quantum mechanics, such as superposition of states, quantum entanglement, wave functions, and equations that determine the energy levels of the layers of the atom. At the end of this article, we use the hydrogen atom as the basis of the representation of the PAL2v model, where the values of the energy levels in six orbital layers are obtained. As an example, we present a possible method of applying the PAL2v model to the use of Raman spectroscopy signals in quality detection of lubricating mineral oil.

Subject Areas

quantum information; shannon entropy; quantum physics; paraconsistent logic; mathematics and computing

Comments (2)

Comment 1
Received: 12 December 2019
Commenter: Paulo Marcelo Tasinaffo
The commenter has declared there is no conflict of interests.
Comment: This article is very interesting and is likely to make major contributions to science because it combines the principles of quantum mechanics formulated in the early twentieth century with recent insights into paraconsistent logic that is nonclassical. As said by the authors of this article: "In this work, we will present an analogy between the modes of use of probability in the Shannon entropy function and the Bernoulli distribution to determine the probability value p of the paraconsistent analysis." I strongly recommend your publication in this high academic journal. Sincerely, Prof. Paulo M. Tasinaffo.
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Response 1 to Comment 1
Received: 16 December 2019
Commenter: João Inácio da Silva Filho
The commenter has declared there is no conflict of interests.
Comment: I thank the commentator for expressing his opinion. Thank you very much.

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