Comment on Statistical mechanics from quantum envariance and exchange symmetry

Abstract

Ojha, Sardana, and Ghosh [Phys. Rev. A 113, 042221 (2026)] propose that tracing environmental records of particle permutations produces an entropy kB ln N!, thereby explaining the Gibbs factor, and use the same construction to multiply the Saha equilibrium relation by 1/(Ne!Np!). We show that these conclusions do not follow. The reduced density matrix printed in their Eq. (32) is not a partial trace, and even under the natural corrected interpretation the entropy equals kB ln N! only when the system branch states are mutually orthogonal. That condition is not generally satisfied and, when imposed on labeled permutation branches, does not by itself restrict the particle state to one bosonic or fermionic symmetry sector. A two-particle calculation makes the contradiction explicit. Their Gibbs-paradox calculation also starts from a distinguishable-particle entropy while calling it the Sackur-Tetrode entropy. In the Saha section, the state in Eq. (52), as written, factorizes and has zero system-environment entanglement. The proposed factorial does not approach unity in the claimed dilute-gas limit, does not yield a finite nonzero intensive thermodynamic limit, and counts indistinguishability twice. We give the corrected canonical and fugacity-based formulations and identify which standard results of the paper remain unaffected.