On the dynamical nature of nonlinear coupling of logarithmic quantum wave equation, Everett-Hirschman entropy and temperature

Abstract

We study the dynamical behavior of nonlinear coupling in a quantum wave equation of a logarithmic type. Using statistical mechanical arguments for a large class of many-body systems, this coupling is shown to be related to temperature which is a thermodynamic conjugate to the Everett-Hirschman's quantum information entropy. A combined quantum-mechanical and field-theoretical model is proposed, which leads to a logarithmic equation with variable nonlinear coupling. We study its properties and present arguments regarding its nature and interpretation, including the connection to Landauer's principle. We also demonstrate that our model is able to describe linear quantum-mechanical systems with shape-changing external potentials.

arXiv comment9 pages

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• Superfluid stars and Q-balls in curved spacetime
• On asymptotic behaviour of galactic rotation curves in superfluid vacuum theory
• Kinks in the relativistic model with logarithmic nonlinearity
• Sound propagation in cigar-shaped Bose liquids in the Thomas-Fermi approximation: A comparative study between Gross-Pitaevskii and logarithmic models
• Acoustic oscillations in cigar-shaped logarithmic Bose-Einstein condensate in the Thomas-Fermi approximation
• Logarithmic wave-mechanical effects in polycrystalline metals: Theory and experiment