Statistical mechanics from quantum envariance and exchange symmetry

TL;DR

This paper demonstrates how fundamental statistical mechanics distributions and concepts can be derived from quantum entanglement and symmetry principles, emphasizing an information-theoretic foundation.

Contribution

It shows that equilibrium structures, including distributions and entropy factors, naturally emerge from quantum envariance and exchange symmetry without additional assumptions.

Findings

Gaussian, Poisson, and Binomial distributions arise from entangled states.

Standard entropy and 1/N! factor are explained via entanglement and indistinguishability.

Classical distributions like Saha, Bose-Einstein, and Fermi-Dirac are derived from quantum symmetry considerations.

Abstract

We build on the foundational work of Deffner and Zurek [S. Deffner and W. H. Zurek, New J. Phys. 18, 063013 (2016)] to show how central equilibrium structures of statistical mechanics can be understood within standard quantum mechanics using the concept of envariance (environment-assisted invariance). In particular, we show how the Binomial, Poisson, and Gaussian distributions naturally emerge from entangled system-environment states. We revisit the Gibbs paradox from a quantum information perspective, demonstrating that the standard Sackur-Tetrode entropy and its 1/N! factor arise from indistinguishability enforced through entanglement with an environment, without introducing additional thermodynamic corrections. Within the same framework, we analyze ionization equilibrium and show how the classical Saha equation is recovered, while clarifying how indistinguishability enters through an entanglement-induced reduction of permutation redundancy. Assuming the standard exchange symmetries of identical quantum particles, we further show how the Bose-Einstein and Fermi-Dirac distributions follow as the equilibrium weighting of symmetry-allowed occupation configurations. Overall, our results support the view that equilibrium statistical mechanics can be consistently interpreted as an emergent consequence of quantum information-theoretic structure and symmetry, rather than as a collection of independent phenomenological postulates.