Principle of least effort vs maximum efficiency: deriving Zipf-Pareto laws

TL;DR

This paper derives Zipf-Pareto laws from the principle of least effort by modeling agents as engines and applying maximum calculus to efficiency, linking thermodynamic concepts to social phenomena.

Contribution

It introduces a probabilistic functional of efficiency and derives Zipf-Pareto laws from thermodynamic principles extended to large agent populations.

Findings

Zipf-Pareto laws derived from efficiency principles

Probabilistic model of efficiency for large agent systems

Application of maximum calculus to efficiency yields known laws

Abstract

This paper provides a derivation of Zipf-Pareto laws directly from the principle of least effort. A probabilistic functional of efficiency is introduced as the consequence of an extension of the nonadditivity of the efficiency of thermodynamic engine to a large number of living agents assimilated to engines, all randomly distributed over their output. Application of the maximum calculus to this efficiency yields the Zipf-Pareto laws.