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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Life as a self-referential deep learning system: A quantum-like Boltzmann machine model.

Yong Tao1

  • 1College of Economics and Management, Southwest University, Chongqing, China.

Bio Systems
|February 28, 2021
PubMed
Summary
This summary is machine-generated.

Human societies exhibit Boltzmann-like income distributions, reflecting swarm intelligence as technological progress. This societal entropy is self-referential, leading to quantum-like behaviors and a novel Boltzmann machine for simulating social organisms.

Keywords:
EntropyQuantum-like Boltzmann machineSelf-referenceSocial organismSwarm intelligence

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Area of Science:

  • Socioeconomics
  • Complexity Science
  • Computational Physics

Background:

  • Empirical studies across 66+ countries reveal market economies follow a Boltzmann-like income distribution.
  • Technological progress in human societies correlates with information entropy.
  • Classical physics entropy differs from societal entropy due to self-reference.

Purpose of the Study:

  • To investigate the relationship between Boltzmann-like income distribution and societal characteristics.
  • To explore the self-referential nature of societal information entropy.
  • To develop a computational model simulating social organism behavior.

Main Methods:

  • Analysis of empirical income distribution data from multiple countries.
  • Theoretical modeling of societal information entropy and its self-referential properties.
  • Construction of a quantum-like Boltzmann machine based on Boltzmann-like income distribution.

Main Results:

  • Human societies with Boltzmann-like income distributions exhibit swarm intelligence, driving technological progress.
  • Societal information entropy is self-referential, distinguishing it from classical physics entropy.
  • The self-reference in societal entropy can induce quantum-like system behavior.

Conclusions:

  • A quantum-like Boltzmann machine can be constructed using Boltzmann-like income distribution.
  • This model can simulate biological behaviors of social organisms, with individuals acting as 'neurons'.
  • Findings bridge socioeconomic patterns with computational models inspired by physics and neuroscience.