Reformulating Chemical Equilibrium in Reacting Quantum Gas Mixtures: Particle Number Conservation, Correlations and Fluctuations

TL;DR

This paper introduces a new framework for describing chemical equilibrium in reactive quantum gas mixtures by enforcing particle number conservation, revealing correlations and fluctuations that extend classical models.

Contribution

It reformulates the canonical ensemble with a global particle-number constraint, naturally deriving correlations and fluctuations in quantum reactive mixtures.

Findings

Correlations emerge across energy eigenstates sharing spin-statistics.

The formalism incorporates concentration fluctuations in the equilibrium state.

Reduces to classical ideal gas behavior in the appropriate limit.

Abstract

The canonical-ensemble description of reactive quantum gas mixtures is reformulated by incorporating a single global particle-number-conservation constraint over the combined spectra of inter-converting species. This constraint replaces the conventional equality of chemical potentials. Fermi-Dirac or Bose-Einstein correlations naturally emerge across one-particle energy eigenstates of species sharing identical spin-statistics, which in ergodic single-systems manifest as intrinsic features of the equilibrium state. By embedding all microstates linked by conversion pathways, the framework incorporates concentration fluctuations in the statistical description. The formalism offers fresh insights into quantum chemical equilibrium in reactive mixtures with composition fluctuations and smoothly reduces to the classical ideal gas limit via an extended partition function that generalizes classical chemical-equilibrium treatments.