Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Application of 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 Shannon Entropy in the Construction of a Paraconsistent Model of the Atom. Preprints 2019, 2019110250 (doi: 10.20944/preprints201911.0250.v2). da Silva Filho, J.I. Application of Shannon Entropy in the Construction of a Paraconsistent Model of the Atom. Preprints 2019, 2019110250 (doi: 10.20944/preprints201911.0250.v2).

Abstract

In this work, we present a model of the atom that is based on a nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The proposed model is constructed with an extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v), which is associated with an interlaced bilattice of four vertices. We use the logarithmic function of the Shannon entropy H(s) to construct the paraconsistent equations and thus adapt a probabilistic model for representations in quantum physics. Through 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 an atom. At the end of this article, we use the hydrogen atom as a 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 the detection of lubricating mineral oil quality.

Subject Areas

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

Comments (1)

Comment 1
Received: 24 February 2020
Commenter: João Inácio Da Silva Filho
Commenter's Conflict of Interests: Author
Comment: In this second version was corrected in the English language and added two algorithms to improve the understanding of the graphical results and applications. Some mathematical-logical relations of fundamentals of physics were also reviewed.
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