Markov models of macrosystems

TL;DR

This paper explores Markov models of macrosystems based on the maximum entropy principle, illustrating their applications across various fields and connecting them to concepts like Nash equilibrium and natural selection.

Contribution

It introduces a framework linking Markov models, maximum entropy, and macrosystem equilibrium, with diverse interdisciplinary applications.

Findings

Maximum entropy principle models macrosystem equilibrium.

Connections between Nash equilibrium, natural selection, and macrosystem equilibrium.

Applications demonstrated in economics, sociology, linguistics, traffic flow, and biology.

Abstract

We collect different examples reflect Bolzman--Jaynes theory of maximum entropy principle. This principle proposed that equillibrium of macrosystem (most probable macrostate of the invariant measure of macrosystem) can be find as a solution of the entropy linear programming problem. Among this examples one can find applications to the economics, sociology, linguistics, traffic flow theory, biology e.t.c. We also describe on examples the connection between Nash's equillibrium, Darwin's principle of natural selection and conception of equillibrium of macrosystem.