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

## TL;DR

This paper explores the nonlinear coupling in a logarithmic quantum wave equation, linking it to thermodynamic temperature and quantum information entropy, and proposes a model connecting quantum mechanics, field theory, and thermodynamics.

## Contribution

It introduces a combined quantum-mechanical and field-theoretical model with variable nonlinear coupling related to temperature and entropy, offering new insights into quantum thermodynamics.

## Key findings

- The nonlinear coupling relates to temperature and entropy in quantum systems.
- The model describes both nonlinear and linear quantum systems with external potentials.
- Connections to Landauer's principle are discussed.

## 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.