Comments on "Mixed Bose-Fermi statistics Kinetic equation and navigation through network" by S.F. Chekmarev, Phys. Rev. E 82, 026106 (2010)

TL;DR

This paper critiques and corrects the kinetic equations and equilibrium distributions for mixed Bose-Fermi statistics in network navigation, clarifying inaccuracies in prior work and providing a valid formulation for certain probability regimes.

Contribution

It presents a corrected kinetic equation for mixed Bose-Fermi systems and derives the proper equilibrium distribution when Fermi move probability is high.

Findings

Previous equations and results were inconsistent with mixed Bose-Fermi statistics.

A new, correct kinetic equation is proposed for the mixture.

The equilibrium distribution is derived for cases with high Fermi move probability.

Abstract

The paper shows that the kinetic equations considered in [1], equilibrium distribution obtained in [1], and results and conclusions obtained on the basis of the kinetic equation derived in [1] do not correspond to the mixed Bose-Fermi statistics. Moreover, it is shown that the kinetic equation corresponding to the case when the copies of the system are characterized by different values of the fraction of the Fermi-like moves is incorrect. We present a correct kinetic equation for the mixture of the Bose and Fermi moves and obtained the equilibrium distribution for the case when the probability of the Fermi moves is higher or equal to that of the Bose moves.