Size limiting in Tsallis statistics

TL;DR

This paper introduces a new model for power law deviations in complex systems by considering size limitations and a decreasing entropy factor, successfully explaining empirical distributions like citation indices and exam scores.

Contribution

It proposes an alternative model where the entropy factor decreases with step size, accounting for size limitations and deviations from power law in complex systems.

Findings

Model explains deviations in power law for large steps.

Application to citation and exam score distributions shows good fit.

Provides insight into size limitations in complex systems.

Abstract

Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered as an important property of these systems. In general, power law exists in the central part of the distribution. It has deviations from power law for very small and very large step sizes. Tsallis, through non-extensive thermodynamics, explained power law distribution in many cases including deviation from the power law, both for small and very large steps. In case of very large steps, they used heuristic crossover approach. In real systems, the size is limited and thus, the size limiting factor is important. In the present work, we present an alternative model in which we consider that the entropy factor q decreases with step size due to the softening of long range interactions or memory. This explains the deviation of power law for very large step sizes. Finally, we apply this model for distribution of citation index of scientists and examination scores and are able to explain the entire distribution including deviations from power law.