Uniqueness of the efficiency functional for deriving the Zipf and the Pareto laws from the principle of least effort

Aziz El Kaabouchi (1) , François-Xavier Machu (2) , Jeremy Cocks (2) , Qiuping A. Wang (3, 2)

1 ESTACA - École Supérieure des Techniques Aéronautiques et de Construction Automobile
2 ESIEA - Ecole Supérieure d'Informatique Electronique Automatique [Paris]
3 IMMM - Institut des Molécules et Matériaux du Mans

In a previous work, we applied the principle of least effort to derive the Zipf and the Pareto power law distributions using a calculus of variation and an efficiency functional. This functional was arrived at by considering living systems containing a great number of agents all trying to achieve something with effort, similarly to thermal engines producing work from source energy, and a nonadditive relationship of efficiency in thermodynamics. In the present work, we provide a complete proof of the uniqueness of this efficiency functional, thus confirms the intrinsic link between the power laws and the principle of least effort.

Mots clés: Least effort; Maximum efficiency; Zipf's law; Pareto's law

Domaines: Mécanique statistique [cond-mat.stat-mech]; Analyse fonctionnelle [math.FA]; Méthodologie [stat.ME]

Aziz El Kaabouchi, François-Xavier Machu, Jeremy Cocks, Qiuping A. Wang. Uniqueness of the efficiency functional for deriving the Zipf and the Pareto laws from the principle of least effort. 2022. ⟨hal-03843384⟩