Non-Equilibrium Quantum Electrodynamics in Open Systems as a Realizable Representation of Quantum Field Theory of the Brain.

Akihiro Nishiyama,Jack A. Tuszynski,Shigenori Tanaka

doi:10.3390/e22010043

Abstract

We derive time evolution equations, namely the Klein–Gordon equations for coherent fields and the Kadanoff–Baym equations in quantum electrodynamics (QED) for open systems (with a central region and two reservoirs) as a practical model of quantum field theory of the brain. Next, we introduce a kinetic entropy current and show the H-theorem in the Hartree–Fock approximation with the leading-order (LO) tunneling variable expansion in the 1st order approximation for the gradient expansion. Finally, we find the total conserved energy and the potential energy for time evolution equations in a spatially homogeneous system. We derive the Josephson current due to quantum tunneling between neighbouring regions by starting with the two-particle irreducible effective action technique. As an example of potential applications, we can analyze microtubules coupled to a water battery surrounded by a biochemical energy supply. Our approach can be also applied to the information transfer between two coherent regions via microtubules or that in networks (the central region and the reservoirs) with the presence of quantum tunneling.

Highlights

What is a physical mechanism of generating memory in the brain, and where is memory stored in the brain? These are still open questions in contemporary neuroscience [1,2]
The aim of this paper is to derive time evolution equations based on quantum electrodynamics (QED) with charged bosons present in open systems in order to provide a theoretical framework for a concrete description of memory formation processes, which can be further developed in the future
We find that time evolution equations in diagonal elements are written only by gauge-invariant functions to the 1st order in the gradient expansion

Summary

Introduction

What is a physical mechanism of generating memory in the brain, and where is memory stored in the brain? These are still open questions in contemporary neuroscience [1,2]. We adopt Shannon entropy as a measure of information content [3]. This entropy increases as the uncertainty associated with information becomes larger. In thermodynamics we use thermodynamic Boltzmannian entropy as a measure of disorder in a physical system. This entropy increases as the order of the system is reduced. There might be no way to memorize information without adopting an ordered physical system as has been earlier discussed within quantum field theory (QFT) [4]. Order is maintained by long-range correlations involving phonons, with Nambu–Goldstone (NG) quanta [6,7,8]

Objectives

Discussion

Conclusion