WH Statistics: Generalized Pauli Principle for Partially Distinguishable Particles

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 λ, exclusion weight \k{appa}, and intrinsic exclusivity γ. 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.

Figures (3)

• Figure 1: Phase diagram of the WHon regime. The color gradient represents the effective exclusion weight $\kappa(T,U)$. The WHon state emerges in the crossover region (yellow) between the unstable bosonic clustering (blue, $\kappa \to 0$) and the rigid fermionic/hard-core limit (red, $\kappa \to 1$), stabilized by the interplay of interaction strength $U$ and thermal energy $k_B T$.
• Figure 2: Thermodynamic anomalies of WHon fluids. (a) Normalized degeneracy pressure $P/P_{cl}$ versus indistinguishability $\lambda$. Unlike Bosons (blue dashed) or Fermions (red dot-dashed), the WHon equation of state (green solid) exhibits a non-monotonic pressure peak. (b) Isochoric specific heat $C_V$. The exclusion-induced statistical gap leads to a Schottky-like anomaly at low temperatures, distinct from the linear behavior of Fermi liquids.
• Figure 3: Generalized HOM interference signatures. (a) Coincidence probability profiles. The WHon state (green/orange lines) exhibits intermediate bunching/anti-bunching behavior tuned by $\kappa$. (b) Statistical modulation of visibility at zero delay. The dashed line represents the WHon prediction, unifying the pure Bose limit ($\kappa=0$) and Fermi limit ($\kappa=1$).