Statistical Physics from Quantum Envariance Principles

TL;DR

This work derives statistical mechanics from quantum envariance, showing that equilibrium distributions and thermodynamic laws follow from entanglement with an environment. By analyzing microcanonical and canonical constructions, it unifies the origins of binomial, Poisson, and Gaussian statistics, and resolves the Gibbs paradox through an entanglement entropy term $S_{ent}=k_B\ln N!$ that enforces indistinguishability. It further derives Bose–Einstein and Fermi–Dirac statistics from envariance-based exchange symmetry and introduces a quantum-corrected Saha equation to account for indistinguishability in ionization equilibrium. The results position statistical mechanics as an emergent discipline grounded in quantum information dynamics, providing a principled mechanism for thermalization and the quantum-to-classical transition with practical implications for dense quantum plasmas and ultracold gases.

Abstract

We build on the foundational work of Deffner and Zurek [S.~Deffner and W.~H.~Zurek, {New J.~Phys.18, 063013 (2016)}] to demonstrate how the principles of statistical mechanics can be derived from 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. Furthermore, we resolve the Gibbs paradox using entanglement entropy, obtaining the Sackur--Tetrode equation with quantum corrections. Extending this framework, we derive a modified Saha equation for ionization equilibrium and recover Bose--Einstein and Fermi--Dirac statistics from quantum symmetries. Our results reinforce and extend the view that statistical mechanics arises as a direct consequence of quantum information dynamics, rather than being founded on phenomenological postulates.