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Statistical Interaction Driven Thermoelectricity and Violation of Wiedemann-Franz Law

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Pith's one-line read A single statistical parameter g is enough to generate thermopower and Wiedemann-Franz violations in quantum point contacts.

desk verdict Sound analytic core with real dualities, but the abstract overclaims the temperature range and the g>1 regime lacks a physical anchor; worth refereeing. read the letter →

arxiv 2506.01930 v1 pith:V23G32HN submitted 2025-06-02 cond-mat.mes-hall

Sampurna Karmakar , Amulya Ratnakar , Sourin Das This is my paper
classification cond-mat.mes-hall
keywords fractionalexclusionstatisticsHaldane-WudistributionSeebeckcoefficientWiedemann-FranzlawLorenznumberthermoelectricfigureofmeritZTparticle-holeasymmetryquantumpointcontact
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that Haldane-Wu fractional exclusion statistics, embodied in a single parameter g that interpolates between bosons (g=0) and fermions (g=1), generate thermoelectric response and Wiedemann-Franz-law violations on their own, with no asymmetry in the scattering profile. For g≠1 the equilibrium occupation function breaks particle-hole symmetry around the chemical potential, quantified by the maximum entropy S_max^g deviating from k_B ln 2 and obeying g S_max^g = $S_max^{{1/g}}$. In linear transport through a quantum point contact with transmission symmetric about the chemical potential, this asymmetry produces a nonzero Seebeck coefficient whose sign is set by ln g, and the Onsager coefficients satisfy a duality under g↔1/g. As a result the Lorenz number deviates from its ballistic value for g>1 across a broad temperature range, while for g≤1 the Wiedemann-Franz law effectively holds, and the figure of merit ZT is enhanced for g>1 and suppressed for g<1. If true, this gives a parameter-free route to thermoelectric conversion from equilibrium statistics alone.

What carries the argument

The central object is the Haldane-Wu distribution for fractional exclusion statistics, η_g(E;µ,T)=1/[W(x,g)+g], with W defined by W(x,g)^g[1+W(x,g)]^{1-g}=e^x and x=(E-µ)/(k_B T). The identity that does the work is the maximum-entropy duality g S_max^g = $S_max^{{1/g}}$, which turns a purely statistical particle-hole asymmetry at the chemical potential into transport asymmetries. The transport-level machinery is the Onsager-coefficient duality L_{α,g}(T)=(-1)^α $g^{{-2}}$ L_{α,1/g}(gT), derived for transmission functions symmetric about the chemical potential, which converts the statistical asymmetry into concrete predictions for the Seebeck coefficient, the Lorenz number, and ZT.

What would settle it

Measure the Seebeck coefficient and Lorenz number of a quantum point contact on a chiral edge whose filling factor is identified with 1/g, with transmission symmetric about the chemical potential. The paper predicts vanishing S for g=1, S of opposite sign for g and 1/g, and Lorenz number L/(g\bar L_0) deviating from unity for g>1 but not for g<1 over a range of temperatures; observing zero S for any g≠1, or a Wiedemann-Franz violation for g<1 stronger than for g>1 under the same transmission profile, would undermine the central claim.

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Extended reading notes

Core claim

The paper establishes that the equilibrium Haldane-Wu occupation function η_g(E;µ,T)=1/[W(x,g)+g] with W(x,g)^g[1+W(x,g)]^{1-g}=e^x, evaluated at the chemical potential, has maximum entropy S_max^g = k_B ln W(0,g)/(g-1), which reduces to k_B ln 2 only at g=1. The duality $S_max^{{1/g}}$ = g S_max^g quantifies the particle-hole asymmetry for g≠1. Transporting these particles through a quantum point contact with transmission symmetric about µ, in linear response, the Onsager coefficients obey L_{α,g}(T)=(-1)^α $g^{{-2}}$ L_{α,1/g}(gT); consequently the Seebeck coefficient vanishes at g=1 and is nonzero with sign of ln g otherwise, the Lorenz number normalized by g\bar L_0 deviates from unity for g>1 across a broad temperature range while approaching unity for g<1, and ZT is enhanced for g>1 and suppressed for g<1.

Load-bearing premise

The load-bearing premise is borrowed from earlier work: charge and heat currents through the point contact are given by Landauer integrals built from the equilibrium Haldane-Wu distribution and its entropy current in linear response, so if excluded-volume correlations beyond the single-particle transmission probability shape the heat current, the predicted dualities, Wiedemann-Franz violations, and ZT values would change.

Editorial extensions

If this is right

  • For g>1 a resonant-level transmission profile yields a Lorenz number that departs from the ballistic value g\bar L_0 over a broad temperature window, i.e., a Wiedemann-Franz violation; for g≤1 the departure is absent or much weaker.
  • The Seebeck coefficient is nonzero for g≠1 and identically zero for g=1 when the transmission function is symmetric about the chemical potential, with the sign equal to the sign of ln g.
  • The figure of merit ZT is substantially enhanced for g>1 and suppressed for g<1, identifying fractional-statistics edges as candidates for thermoelectric energy conversion.
  • The Onsager coefficients obey L_{α,g}(T)=(-1)^α g^{-2} L_{α,1/g}(gT), so a system with parameter g and the dual system 1/g exchange thermopower sign and rescale their response.
  • In the ballistic limit the Lorenz number scales as L = g\bar L_0, so a generalized Wiedemann-Franz law holds up to the statistical factor g.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An implicit experimental handle: in a fractional quantum Hall edge where the filling fraction ν plays the role of 1/g, the predicted sign change of the Seebeck coefficient under g↔1/g could be used to identify the statistical parameter from transport alone.
  • The maximum-entropy diagnostic may transfer to other settings: any equilibrium distribution whose occupancy at the chemical potential deviates from 1/2, such as generalized exclusion processes, would be predicted to show the same thermoelectric asymmetry when coupled to a symmetric scatterer.
  • The duality at scaled temperature suggests a concrete comparative experiment: measure S and L of a g-system at temperature T and of the complementary 1/g system at temperature gT, where the paper's relations predict exact correspondence.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The manuscript studies linear-response transport of particles obeying Haldane–Wu fractional exclusion statistics through a quantum point contact. It identifies particle–hole asymmetry in the Wu occupation function, derives duality relations L_{α,g}(T)=(-1)^α g^{-2} L_{α,1/g}(gT) and their consequences for the electrical conductance, thermal conductance, Seebeck coefficient, and Lorenz number, and evaluates the thermoelectric figure of merit ZT for a resonant-level transmission model. The central numerical claims are that the Seebeck coefficient changes sign under g↔1/g, that the g-scaled Lorenz number deviates from unity for g>1 while staying close to unity for g≤1, and that ZT is enhanced for g>1 and suppressed for g<1.

Significance. If correct, the paper provides a minimal mechanism—statistical interaction alone, without an engineered scattering asymmetry—for thermoelectric response and Lorenz-number deviations in chiral edge systems, with a falsifiable duality signature. The derivation of the duality relations (8)–(13) is internally consistent and the sign reversal of the Seebeck coefficient is a crisp, testable prediction. However, the advertised temperature-range and Wiedemann–Franz-violation dichotomy is not actually demonstrated by the data as presented, and the paper's use of the term 'Wiedemann–Franz violation' needs to be calibrated against the standard L=L0 reference.

major comments (2)
  1. [Lorenz number, Fig. IV] The abstract claims significant Wiedemann–Franz violations for g>1 that are absent for g≤1 'across a broad temperature range,' but the only Lorenz-number data shown, Fig. IV, is a scan over the transmission width σ at fixed T=1 K. Equation (13) relates L_g(T)/(g L0) to L_{1/g}(gT)/((1/g) L0), so temperature enters through a rescaled argument; a σ-scan at a single temperature cannot establish persistence across a temperature range. The body text itself only claims 'a finite temperature range for an appropriately chosen value of σ.' Either add temperature sweeps demonstrating that the g>1 deviation persists and the g<1 case remains near unity, or temper the abstract's 'broad temperature range' claim.
  2. [Lorenz number, Eq. (13) and Fig. IV] The paper's notion of Wiedemann–Franz 'violation' is non-standard and should be stated precisely. In the ballistic limit with energy-independent transmission the authors find L=g L0, so for any g≠1 the ordinary Lorenz number already differs from the standard Fermi-liquid value L0. The quantity plotted in Fig. IV is L/(g L0), i.e., the deviation from the g-scaled reference, not from L0. With the g-scaled reference the statement 'violations arise for g>1 but remain absent for g≤1' may hold; with the standard reference L=L0 it does not, because g<1 also gives L≠L0 in the ballistic limit. The abstract should specify that the dichotomy refers to deviations from g L0 rather than from the conventional Wiedemann–Franz value.
minor comments (4)
  1. [Fig. IV caption] The caption is incomplete: it reads 'by varying the width σ=.' with no value or range, and the axes are not labeled in the figure as described. Please complete the caption and label the axes.
  2. [Fig. III and Eq. (11)] The paper states that the choice of g values probes the duality relation, but the plotted temperatures (T=1 K and T=1.5 K) do not directly test Eq. (11), which relates S_g(T) to -g S_{1/g}(gT). A comparison at paired temperatures, for example S_3(1 K) versus -3 S_{1/3}(3 K), would make the duality verification explicit.
  3. [Appendix B, Eq. (B6)] The simplification from Eqs. (B4)–(B5) to Eq. (B6) is stated as 'in linear response and using (A1),(A2) it can be shown,' but the intermediate algebra is not displayed. Since this step underlies the heat current and therefore the Lorenz number and ZT results, a short derivation in the appendix would improve transparency.
  4. [Acknowledgments] There is a typo in the acknowledgments: 'recieved' should be 'received.'

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the transport dualities and WF/ZT statements are derived from stated Haldane–Wu premises, with self-citations used only for motivation and consistency checks.

full rationale

The derivation chain is self-contained and non-circular. Starting from the Wu distribution (Eq. 1) and the Nayak–Wilczek duality (Eq. 2), the paper derives the maximum-entropy duality (Eq. 4), the Onsager integrals (Eq. 7) using the transport formalism of Ref. [18], and then obtains the transport dualities (Eqs. 8–13) as algebraic consequences for transmission symmetric about the chemical potential. The Lorenz number and ZT are evaluated from these integrals for explicit transmission functions with free parameters g, σ, Γ, and T; no quantity is fitted to a subset of data and then renamed a prediction. The self-citations (Ref. [16] as motivation and Ref. [26] as a ballistic-limit consistency check) are not load-bearing: the ballistic Lorenz scaling L = g L̄0 is re-derived from the paper's own integrals (L0 = (1/hg)t, L2 = π²kB²T²/3h t). The only flagged discrepancy is between the abstract's 'broad temperature range' and the body's own statement of WF violations 'across a finite temperature range for an appropriately chosen value of σ', with Fig. IV being a σ-scan at T = 1 K. That is a support-strength or correctness concern about temperature extrapolation, not a circular reduction: Eq. (13) is a derived symmetry relation, not an assumed target. No circular step can be exhibited, so the circularity score is 0.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claims rest on the Haldane-Wu distribution (prior literature), the Landauer-with-HES transport assumption (borrowed from Ref. 18), the Nayak-Wilczek duality (prior literature), and a symmetric transmission window (assumed in this paper). No parameter is fitted to experimental data; g, sigma, Gamma, T, and mu-tilde are scanned or chosen by hand, and the interesting effects are parametric in these choices. The derivation itself is closed-form and checkable, and no new particles, forces, dimensions, or conserved quantities are introduced.

free parameters (4)
  • g (statistical interaction parameter) = scanned over 1/5, 1/3, 1, 3, 5, not fitted
    Control parameter of Haldane-Wu statistics; all central claims (PHS breaking, WF asymmetry, ZT enhancement) are functions of g. No value is fitted to data.
  • sigma (transmission window width) = varied in Figs. III-IV, full width of the window function in Eq. (12)
    Chosen by hand to illustrate the finite-window Lorenz-number deviation; the WF-violation claim depends on sigma being finite, so its value is load-bearing.
  • Gamma (quantum dot resonance width) = 0.01 meV (Fig. V)
    Chosen by hand for the Lorentzian transmission t_qd(E); the reported maximum ZT values depend on this width.
  • T and mu (temperature and chemical potential) = T=1K (1.5K in Fig. III), mu=1.3 meV
    Environmental parameters chosen for the plots; the 'broad temperature range' claim rests on how the deviation varies with T, which is shown at only two temperatures.
assumptions (5)
  • domain assumption Haldane-Wu occupation function (Eq. 1) is the equilibrium distribution of fractional exclusion statistics particles.
    Taken from Refs. 5 and 13; it is the input theory, not derived in this paper.
  • domain assumption Landauer transport formulas apply to HES particles (charge current Eq. B3, entropy current Eqs. B4-B5).
    Invoked via Ref. 18 ('transport coefficients... follow the same general expressions'); this is the load-bearing premise behind all L_alpha integrals.
  • standard math Nayak-Wilczek duality, Eq. (2): 1 - g eta_g(x) = (1/g) eta_{1/g}(-x/g).
    Prior result (Ref. 14) from which the entropy and transport dualities are derived.
  • ad hoc to paper Transmission function symmetric about mu for the duality relations (Eqs. 8-13).
    Explicitly assumed ('we focus on the case where the transmission function is symmetric with respect to the system's chemical potential'); the sign and g-asymmetry claims rely on it.
  • standard math Lower energy bound E(0) = -infinity in the transport integrals.
    Stated in Appendix A; valid when the band bottom lies well below the thermal excitation window.

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Pith. "Pith review of Statistical Interaction Driven Thermoelectricity and Violation of Wiedemann-Franz Law." pith.science (2026). https://pith.science/paper/V23G32HN

@misc{pith2026250601930,
  author       = {Pith},
  title        = {Pith review of: Statistical Interaction Driven Thermoelectricity and Violation of Wiedemann-Franz Law},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V23G32HN}},
  note         = {Machine review of arXiv:2506.01930}
}
abstract

Quantum transport anomalies in systems obeying Haldane-Wu fractional exclusion statistics, characterized by the statistical interactions parameter $g$ are investigated. We identify particle-hole symmetry breaking of the Haldane-Wu distribution function via its deviations of the maximum entropy ($\mathcal{S}_{g}^{max}$), evaluated at the chemical potential, from the value ${k_B} \ln 2$ (a value that holds only at the free fermion limit, $g=1$). A duality relation, $g\,\mathcal{S}_{g}^{max}=\mathcal{S}_{1/g}^{max}$, quantifying the degree of violation is obtained. This symmetry breaking manifests in transport phenomena as: significant violations of the Wiedemann-Franz law arising for $g>1$ (but remain absent for $g\leq 1$) across a broad temperature range. Moreover, the thermoelectric figure of merit $ZT$ is substantially enhanced for $g>1$ and suppressed for $g<1$, indicating new routes to optimize energy conversion. These results deepen the understanding of the interplay between equilibrium statistics and transport, suggesting avenues for engineering advanced thermoelectric materials.

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