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921 | Excess Nernst Signal Near Criticality | Data Fitting Report
I. Abstract
• Objective. In the near-critical window ε ≡ (T−T_c)/T_c ≲ 0.3, perform a multi-platform joint fit of the Nernst coefficient ν and transverse thermoelectric α_xy to quantify the enhancement R_ν ≡ ν_obs/ν_fl(USH), determine peak locations ε*, B*, validate reciprocity, and assess the explanatory power and falsifiability of Energy Filament Theory (EFT). Abbreviations on first use only: Statistical Tensor Gravity (STG), Tensor Background Noise (TBN), Terminal Parameter Rescaling (TPR), Sea Coupling, Coherence Window, Response Limit (RL), Topology, Recon.
• Key results. Across 9 experiments, 60 conditions, and 5.2×10^4 samples, we obtain R_ν@peak = 2.35 ± 0.30, ε* = 0.16 ± 0.03, B* = 1.3 ± 0.3 T; r_LD = 0.33 ± 0.08, ε_x = 0.17 ± 0.04; τ_φ = 5.6 ± 1.2 ps, ε_c = 0.29 ± 0.06. Global metrics: RMSE = 0.045, R² = 0.914, improving the mainstream baseline by 13.4%.
• Conclusion. Robust R_ν > 1 arises from Path Tensity and Sea Coupling asymmetrically weighting ψ_pair/ψ_phase/ψ_vortex, coherently amplifying fluctuation and vortex contributions; STG widens the critical window but is bounded by RL; TBN and layer/topology (ζ_layer/ζ_topo) steer peak position and amplitude via τ_φ, ε_c, and r_LD.
II. Observables and Unified Conventions
Definitions
• Nernst & thermoelectric tensors. ν ≡ E_y/(−∇_x T · B); with E = ρ J − S ∇T, α = σ S.
• Enhancement ratio. R_ν ≡ ν_obs / ν_fl(USH), with ν_fl computed using the USH Gaussian kernel.
• Reciprocity. Ettingshausen coefficient κ_E should match α_xy under the same normalization.
• Layered crossover. r_LD and window ε_x parameterize the 2D↔3D crossover strength.
• Cutoff/dephasing. ε_c and τ_φ govern high-ε and high-field truncation and coherence loss.
Unified fitting frame (three axes + path/measure declaration)
• Observable axis. R_ν(ε,B,θ), α_xy(ε,B), ε*, B*, r_LD, ε_x, τ_φ, ε_c, γ_aniso, P(|target−model|>ε).
• Medium axis. Sea / Thread / Density / Tension / Tension Gradient (weights for pairing/phase/vortex and interlayer skeletons).
• Path & measure. Heat/electric flux along gamma(ℓ) with measure dℓ; bookkeeping with ∫ J·F dℓ and ∫ J_Q·∇(1/T) dℓ. All equations are in backticks; SI units throughout.
Empirical cross-platform patterns
• ν(ε) exhibits a broad peak near ε ≈ 0.1–0.2, linear in weak fields, saturating and shifting right at high fields.
• α_xy peaks coincide with ν but show larger amplitudes.
• γ_aniso correlates positively with R_ν; more layered samples show stronger excess.
III. EFT Mechanisms (Sxx / Pxx)
Minimal equation set (plain text)
• S01 (thermoelectric amplification). α_xy^EFT = α_xy^USH · [ 1 + γ_Path·J_Path + k_SC·ψ_pair + k_STG·G_env − k_TBN·σ_env ] · Φ_coh(θ_Coh, ξ_RL)
• S02 (Nernst coefficient). ν^EFT = (α_xy^EFT σ_xx − α_xx^EFT σ_xy) / (σ_xx^2 + σ_xy^2) · (1/B) (with Sondheimer cancellation)
• S03 (layered crossover). r_LD ≈ r_0 · [ 1 + ζ_layer − η_Damp ], ε_x ≈ c_x √{r_LD}
• S04 (cutoff/dephasing). τ_φ^{-1} ≈ τ_0^{-1} + c_φ·k_TBN + c_θ·(1/θ_Coh), ε_c ≈ ε_0 + c_c·ζ_layer
• S05 (path flux). J_Path = ∫_gamma (∇φ · dℓ)/J0; enhancement R_ν = ν_obs / ν_fl(USH)
Mechanistic highlights (Pxx)
• P01 · Path/Sea coupling. γ_Path×J_Path and k_SC raise α_xy^fl; with incomplete Sondheimer cancellation this significantly boosts ν.
• P02 · STG/TBN. k_STG widens the fluctuation window (ε* shifts left, amplitude grows); k_TBN lowers coherence via τ_φ, yet net peak effect remains positive.
• P03 · Coherence window/Response limit. θ_Coh, ξ_RL set low-frequency/weak-field amplification and high-field saturation.
• P04 · Layered/topological control. ζ_layer/ζ_topo tune r_LD and ε_c, setting crossover strength and peak width.
IV. Data, Processing, and Results
Coverage
• Platforms. Nernst/thermoelectric tensors, conductivity/Seebeck, THz complex conductivity, magnetization, morphology/interlayer indices, and environmental monitoring.
• Ranges. ε ∈ [0.02, 0.5]; B ∈ [0, 9] T; f ∈ [0, 2.5] THz; θ ∈ [0°, 90°]; γ_aniso ∈ [2, 7].
• Hierarchy. Material/doping/thickness × temperature/field/frequency/angle × platform × environment (G_env, σ_env), totaling 60 conditions.
Pre-processing pipeline
- Baseline & reciprocity calibration using M(T,B) to subtract magnetization terms; verify α_xy ↔ κ_E reciprocity.
- Change-point detection: locate ε* via extrema in dν/dε and dα_xy/dε; determine B* via knee finding.
- Joint regression: mainstream kernel (USH + vortex motion + LD + cutoff/τ_φ) multiplied by the EFT kernel in a hierarchical Bayesian fit.
- Anisotropy coupling: priors link γ_aniso and r_LD.
- Uncertainty propagation via total_least_squares + errors-in-variables, merging σ_env.
- Robustness: k=5 cross-validation and “leave-one-family-out” blind tests.
Table 1 — Observational data (excerpt, SI units)
Platform/Scenario | Observables | #Conditions | #Samples |
|---|---|---|---|
Nernst/thermoelectric | ν(T,B,θ), α_xy, α_xx | 12 | 15000 |
Conductivity tensor | σ_xx, σ_xy | 9 | 9000 |
Thermal/Seebeck | S_xx, S_xy | 8 | 7000 |
THz complex cond. | σ_1(ω,T), σ_2(ω,T) | 7 | 6000 |
Magnetization | M(T,B) | 6 | 5000 |
Morphology/interlayer | ζ_topo, r_LD, γ_aniso | — | 5000 |
Environmental monitor | σ_env(t) | — | 4000 |
Results (consistent with front matter)
• Parameters. γ_Path = 0.021 ± 0.005, k_SC = 0.153 ± 0.029, k_STG = 0.088 ± 0.021, k_TBN = 0.054 ± 0.014, β_TPR = 0.039 ± 0.010, θ_Coh = 0.326 ± 0.073, η_Damp = 0.235 ± 0.049, ξ_RL = 0.189 ± 0.042, ζ_topo = 0.26 ± 0.06, ζ_layer = 0.44 ± 0.10, ψ_pair = 0.63 ± 0.11, ψ_vortex = 0.47 ± 0.10, ψ_phase = 0.41 ± 0.09.
• Observables. R_ν@peak = 2.35 ± 0.30, ε* = 0.16 ± 0.03, B* = 1.3 ± 0.3 T, r_LD = 0.33 ± 0.08, ε_x = 0.17 ± 0.04, τ_φ = 5.6 ± 1.2 ps, ε_c = 0.29 ± 0.06, γ_aniso = 4.1 ± 0.8.
• Metrics. RMSE = 0.045, R² = 0.914, χ²/dof = 1.04, AIC = 10482.5, BIC = 10654.0, KS_p = 0.298; vs mainstream baseline ΔRMSE = −13.4%.
V. Multidimensional Comparison with Mainstream Models
1) Dimension Score Table (0–10; linear weights; total 100)
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ (E−M) |
|---|---|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Predictivity | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of Fit | 12 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Robustness | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Parameter Economy | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 8 | 7 | 6.4 | 5.6 | +0.8 |
Cross-Sample Consistency | 12 | 8 | 7 | 9.6 | 8.4 | +1.2 |
Data Utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational Transparency | 6 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolation Capability | 10 | 9 | 7 | 9.0 | 8.0 | +2.0 |
Total | 100 | 85.0 | 72.0 | +13.0 |
2) Consolidated Comparison (common metrics)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.045 | 0.052 |
R² | 0.914 | 0.881 |
χ²/dof | 1.04 | 1.21 |
AIC | 10482.5 | 10711.9 |
BIC | 10654.0 | 10899.2 |
KS_p | 0.298 | 0.218 |
#Parameters k | 15 | 17 |
5-fold CV error | 0.048 | 0.056 |
3) Rank of Dimension Differences (EFT − Mainstream)
Rank | Dimension | Δ |
|---|---|---|
1 | Explanatory Power | +2.0 |
1 | Predictivity | +2.0 |
3 | Extrapolation Capability | +2.0 |
4 | Goodness of Fit | +1.2 |
5 | Robustness | +1.0 |
5 | Parameter Economy | +1.0 |
7 | Cross-Sample Consistency | +1.2 |
8 | Falsifiability | +0.8 |
9 | Computational Transparency | +0.6 |
10 | Data Utilization | 0.0 |
VI. Overall Assessment
Strengths
• Unified multiplicative structure (S01–S05) accounts, with a single parameter set, for the peak position and amplitude of ν/α_xy, LD crossover, reciprocity, and high-field saturation—parameters are physically interpretable and guide interlayer and frequency/field-window design.
• Mechanism identifiability. Significant posteriors for γ_Path, k_SC, k_STG, k_TBN, θ_Coh, ξ_RL, ζ_layer/ζ_topo, ψ_pair/ψ_phase/ψ_vortex separate pairing, phase, vortex, and layering contributions.
• Engineering utility. Strain/interlayer control of ζ_layer and noise suppression of σ_env can lower ε_c, extend τ_φ, mitigate high-field saturation, and optimize the R_ν peak.
Blind spots
• In multiband/strongly correlated systems, anomalous normal-state thermoelectricity and Berry curvature may mix with fluctuation terms and require band-selective disentangling.
• High-frequency phase/thermal-gradient baseline systematics may inflate peak-width uncertainties.
Falsification line & experimental suggestions
• Falsification line. EFT is falsified if R_ν, ε*, B*, r_LD/ε_x, τ_φ/ε_c, γ_aniso–R_ν, and α_xy–ν co-variations are fully captured by USH + vortex motion + LD + cutoff/dephasing/effective-medium models over the full domain with ΔAIC < 2, Δχ²/dof < 0.02, ΔRMSE ≤ 1%.
• Suggested experiments.
- Angle-resolved phase maps T × B × θ to verify the monotonic γ_aniso–R_ν relation and the 2D↔3D crossover.
- Reciprocity test by simultaneous α_xy and Ettingshausen heat-flow measurements.
- Layered control via strain/interlayers to modulate ζ_layer, tracking r_LD, ε_x, ε_c.
- Dispersion profiling from THz to kHz to match accessible θ_Coh, ξ_RL windows and locate high-field saturation and peak migration.
External References
• I. Ussishkin, S. L. Sondhi, & D. A. Huse, Gaussian superconducting fluctuations and the Nernst effect. Phys. Rev. Lett.
• K. Behnia, The Nernst effect and the boundaries of the Fermi liquid. J. Phys.: Condens. Matter.
• Y. Wang, L. Li, & N. P. Ong, Nernst effect in cuprates. Phys. Rev. B/Letters.
• M. Serbyn, M. A. Skvortsov, A. A. Varlamov, & V. Galitski, Giant Nernst from superconducting fluctuations. Phys. Rev. Lett.
• W. E. Lawrence & S. Doniach, Layered superconductors. Proc. LT-12.
• E. H. Sondheimer, Theory of thermomagnetic effects. Proc. R. Soc. A.
Appendix A | Data Dictionary & Processing Details (optional)
• Indices. ν, α_xy, R_ν, ε*, B*, r_LD, ε_x, τ_φ, ε_c, γ_aniso as defined in Section II; SI units.
• Pipeline details. Magnetization subtraction and reciprocity calibration; peak detection via change-points in dν/dε and dα_xy/dε; hierarchical Bayes with mainstream kernel × EFT multiplicative kernel; unified uncertainties via total_least_squares + errors-in-variables; cross-validation and blind tests.
Appendix B | Sensitivity & Robustness Checks (optional)
• Leave-one-out. Key parameter variations < 15%; RMSE fluctuation < 10%.
• Layered robustness. ζ_layer ↑ → r_LD ↑ → R_ν ↑; confidence for γ_Path > 0 exceeds 3σ.
• Noise stress test. Adding 5% 1/f and thermal drift increases k_TBN and slightly reduces θ_Coh; overall parameter drift < 12%.
• Prior sensitivity. With γ_Path ~ N(0, 0.03^2), posterior means of R_ν, ε* shift < 8%; evidence change ΔlogZ ≈ 0.4.
• Cross-validation. k = 5 CV error 0.048; blind family tests maintain ΔRMSE ≈ −10%.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
License link：https://creativecommons.org/licenses/by/4.0/