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

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.

Shannon entropy along hydrogen isoelectronic sequence using Numerov method

“…The range of applicability has been extensively extended to atomic, molecular and nuclear spectroscopy including study of different properties like ionization potential, global delocalization, molecular geometric parameters, reaction paths and highly excited states of single particle systems [15][16][17][18][19]. Filho [20] used hydrogen atom as a basis to demonstrate the use of Shannon entropy in a paraconsistent model for modeling quantum systems. Entropy minimisation approach is applied to remove specularities from imaging spectroscopy data [21].…”