Life as a self-referential deep learning system: A quantum-like Boltzmann machine model

Abstract

It has been empirically found that the income structure of market-economy societies obeys a Boltzmann-like income distribution. The empirical evidence has covered more than 66 countries. In this paper, we show that when a human society obeys a Boltzmann-like income distribution, it resembles a social organism in which the swarm intelligence in humans is reflected as technological progress. Also, we have verified that the technological progress stands for the information entropy of a human society. However, differing from the entropy in classical physics, we show that the entropy in a human society is self-referential. In particular, we find that the self-reference might change a classical physical system into a quantum-like system. Based on this finding, we employ the Boltzmann-like income distribution to construct a quantum-like Boltzmann machine. Here, we propose to use it to simulate the biological behaviors of a social organism in which each social member plays a role analogous to that of a neuron within a brain-like architecture.