675 – Advances in Time Series Analysis

The Inequality Process Is 'Demonic': Conditional Entropy Maximization and Minimization and Wage Incomes

at Inequality Process Institute

Maxwell's Demon intervenes into the Kinetic Theory of Gases (KTG), a particle system, removing particles with above mean kinetic energy, decreasing the entropy of the remaining particles. The Teacher intervenes into the Inequality Process (IP), a particle system of wealth distribution whose stationary distribution is approximated by a gamma pdf. An IP particle's probability of having its parameter retired by the Teacher is inversely proportional to its wealth. The Teacher replaces each retired particle parameter with that of a particle whose probability of selection is proportional to its wealth. The IP tends to transfer wealth to particles with small values of the particle parameter, by hypothesis of the IP's meta-theory and evidence representative of more productive workers. Teacher-driven evolution of the IP begins with large particle parameter values that the IP's meta-theory attributes to the earliest civilizations. Teacher-driven IP evolution reproduces features of the distribution of labor income over techno-cultural evolution, including the last half century in the U.S. Teacher-driven change in the IP's stationary distributions results in higher entropies of particle wealth. These increases in the entropy of particle wealth decelerate as the stationary distributions become more centralized. Simultaneously, the Teacher drives the increasing absolute value of the correlation between particle wealth and the particle parameter. This effect eventually decreases particle wealth entropy. This finding suggests that empirical analogues of Teacher and IP turn entropy increase in worker income and wealth into information gain over the course of technological evolution.