WH Statistics: Generalized Pauli Principle for Partially Distinguishable Particles

TL;DR

WH Statistics introduces a unified framework for particle statistics that interpolates between classical and quantum behaviors, capturing partial distinguishability and exotic phenomena like non-monotonic degeneracy pressure.

Contribution

This work develops a novel theoretical framework that generalizes particle statistics to include partial distinguishability and introduces WHons with unique physical properties.

Findings

Recovers Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann statistics

Predicts non-monotonic degeneracy pressure peaks and Schottky-like anomalies

Provides a bridge between quantum and classical exclusion principles

Abstract

Traditional statistical mechanics is constrained by the binary paradigms of identical/distinguishable and bosonic/fermionic particle statistics, leading to a fundamental logical gap in describing systems with partial distinguishability. We propose WH Statistics, a unified theoretical framework governed by three key parameters: continuous distinguishability {\lambda}, exclusion weight \k{appa}, and intrinsic exclusivity {\gamma}. By deriving the microstate count and entropy, we show that this framework naturally recovers the Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann statistics, while also incorporating anyons and the classical hard-core (Langmuir) limit. We introduce a class of generalized quasiparticles, termed WHons, which exhibit exotic physical phenomena including non-monotonic degeneracy pressure peaks, Schottky-like specific heat anomalies, and tunable interference effects, driven by the interplay between fractional distinguishability and exclusion. This framework bridges the century-old discontinuity between quantum and classical exclusion principles, providing a powerful tool for investigating strongly correlated systems and programmable quantum matter.