Wh Statistics Achieves Unified Framework with Λ, \k{appa} & Γ Parameters

Researchers are challenging the foundations of statistical mechanics with a new framework to describe particles that aren’t strictly identical or distinguishable. Wang Hao, Meng Yancen, and Zhang Kuang, all from the School of Electronics and Information Engineering at Harbin Institute of Technology, alongside Zhou Rui’en, present ‘WH Statistics’ , a generalised approach incorporating parameters for continuous distinguishability, exclusion weight, and intrinsic exclusivity. This work is significant because it elegantly unifies Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann statistics under one umbrella, extending to encompass anyons and classical limits, and predicts exotic behaviours from newly defined ‘WHons’ , quasiparticles exhibiting unusual pressure and heat characteristics. By bridging the gap between quantum and classical exclusion principles, WH Statistics offers a powerful new lens through which to investigate complex, strongly correlated quantum systems.

The core of this innovation lies in treating particle indistinguishability as a continuous degree of freedom, represented by λ, ranging from 0 to 1. This parameter elegantly bridges the gap between fully distinguishable classical particles and strictly identical quantum particles, defined microscopically by the wavefunction overlap λ ≡|⟨ψi|ψj⟩|2.

Furthermore, the researchers quantified the competition between quantum exclusion and thermal fluctuations using an effective exclusivity weight, κ, linked to microscopic interaction strength and temperature through a Padé approximant evolution equation. The introduction of a discrete topological parameter, γ, characterizing intrinsic exchange symmetry, completes the framework, allowing for a comprehensive description of particle behaviour. Experiments show that the resulting WH entropy, maximized under particle and energy conservation, leads to an implicit transcendental equation for the average occupation number, ultimately defining the unified WH distribution function. This function accurately reproduces standard statistical limits at specific boundaries, with fermions and bosons emerging as natural bifurcations of the framework. Notably, the study resolves the microscopic origin of the classical hard-core limit, demonstrating that the unity term in the Langmuir distribution arises strictly from classical steric exclusion, clarifying a foundational concept in surface science.

WH Statistics and Generalized Particle Behaviour are crucial

Scientists developed WH Statistics, a novel theoretical framework addressing limitations within traditional statistical mechanics concerning partially distinguishable particles. These anomalies follow a scaling of Tpeak ∝ κ/ ln(1/λ), offering a spectroscopic method for extracting the microscopic parameters λ and κ. Experiments employed a generalized Hong-Ou-Mandel (HOM) probability equation: PHOM(∆x, κ) = 1 −exp ” − ∆x βλdB 2# cos(πκ), to investigate interference patterns, revealing that the temporal width is limited by geometric decoherence (λdB) and the saturation amplitude is governed by κ. This statistically constrained decoherence suggests anyon collision experiments function as HOM interferometers, potentially exhibiting vanishing interference signals at statistical critical points.

Furthermore, the research team demonstrated that WHons adhere to a “Soft Blockade” principle, where finite λ allows spatial overlap, but repulsion from κ →1 enforces long-range anti-correlations, creating a statistically forbidden region of 0g(2)(0) 0.5. Near the critical pressure point λc, the correlation function transitions from exponential to power-law decay, stabilizing an exceptional fermionic superfluid state. By interpreting λ as an ensemble average over discrete rational configurations, scientists reconciled macroscopic continuity with integer microstate counts, predicting stepwise transitions in finite-size systems. The exclusion weight κ was established as a rigorous order parameter, linked to the ratio of interaction energy to thermal fluctuations, while intrinsic symmetry γ remains strictly discrete due to 3D permutation group topology.

WH Statistics unifies particle indistinguishability descriptions with quantum

Scientists have developed WH Statistics, a novel theoretical framework addressing the limitations of traditional statistical mechanics by incorporating partial distinguishability between particles. The unified microscopic configuration number, ΩWH, for N particles occupying G states is constructed as: ΩWH = 1 (N!)λ G + (1 −κ)(1 −γ)(N −1) G −κN −(1 −κ)(1 −γ) . Applying Stirling’s approximation in the thermodynamic limit (N, G ≫1) yields the generalized WH entropy: SWH ≈kB h A ln A −B ln B −λ(N ln N −N) i, where A ≡G + κN and B ≡G −κN. Crucially, the term −λkB(N ln N −N) functions as a tunable Gibbs correction factor, resolving the mixing entropy paradox within a continuous manifold.

Results demonstrate that maximizing SWH under particle and energy conservation yields the implicit transcendental equation for the average occupation number nWH = N/G: β(ε −μ) = ln (1 + κnWH) κ(1 −κnWH)−κ nλ WH. This solution parameterizes into the unified WH distribution function, nWH(ε) = 1 eβ(ε−μ) + Θ(κ, γ, nWH), where Θ(κ, γ, n) ≡1 n 1 −n1−λ(1 + κn) κ(1 −κn)κ.