Decay Entropy Scaling of Radionuclide Intervention Efficacy in Unsaturated Soil Profiles: A Theoretical Model
Abstract
The relationship between radionuclide contamination depth and subsurface intervention efficacy remains theoretically unconstrained. Conventional intuition assumes monotonic efficacy decline with depth due to increased transport pathlength and attenuation. To derive a mathematically rigorous, falsifiable relationship between depth‑dependent decay entropy and intervention efficacy in unsaturated soils, explicitly challenging the depth‑inverse efficacy paradigm. A coupled advection‑dispersion‑decay model (1‑D semi‑infinite domain, constant water flux, homogeneous porous medium) is formulated with a novel decay entropy metric – defined as the Shannon entropy of the radionuclide age distribution at depth . The intervention (step reduction of surface source by fraction at yields a time‑integrated efficacy , where is the instantaneous relative concentration reduction. Using the Green’s function solution for a flux boundary and the age probability density (with ), we prove that . For fixed mean age, the integral decreases monotonically with increasing entropy . Consequently: where depends on . This predicts higher efficacy at greater depth because broader age distributions (higher ) increase the fraction of radionuclides with ages – i.e., those already affected by the source reduction. Deeper contamination () is more responsive to surface‑applied interventions (e.g., capping, phytoremediation, chemical injection) than shallower contamination – exactly opposing conventional wisdom. A complete experimental design is provided (Section 2.6): 20 soil cores to 1 m, sectioned every 10 cm; compute from ¹³⁷Cs activity profile (λ = 2.3×10⁻² yr⁻¹); apply surface source‑reduction treatment; monitor dissolved ¹³⁷Cs at 10, 30, 60, 90 cm depth for two years; test positive correlation between and . Negative or null correlation falsifies the model. Two Testable Policy‑Relevant Predictions: (1) Depth‑integrated radionuclide activity is a superior predictor of remediation success than surface activity (2) Decay entropy gradients can zone sites for intervention priority (highest → highest efficacy). A complete, mathematically explicit, falsifiable theoretical framework linking decay entropy to intervention efficacy in unsaturated soils.
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BibTeX
@article{adiaha2026decay,
title = {{Decay Entropy Scaling of Radionuclide Intervention Efficacy in Unsaturated Soil Profiles: A Theoretical Model}},
author = {Monday Sunday Adiaha},
journal = {Manatri: Journal of Multi-Disciplinary Research},
year = {2026},
month = sep,
doi = {10.4038/manatri.v2i2.3},
url = {https://hal.science/hal-05768107v1},
note = {CC BY-ND 4.0},
}
RIS
TY - JOUR
TI - Decay Entropy Scaling of Radionuclide Intervention Efficacy in Unsaturated Soil Profiles: A Theoretical Model
AU - Monday Sunday Adiaha
PY - 2026
DA - 2026/09/28
JO - Manatri: Journal of Multi-Disciplinary Research
DO - 10.4038/manatri.v2i2.3
UR - https://hal.science/hal-05768107v1
AB - The relationship between radionuclide contamination depth and subsurface intervention efficacy remains theoretically unconstrained. Conventional intuition assumes monotonic efficacy decline with depth due to increased transport pathlength and attenuation. To derive a mathematically rigorous, falsifiable relationship between depth‑dependent decay entropy and intervention efficacy in unsaturated soils, explicitly challenging the depth‑inverse efficacy paradigm. A coupled advection‑dispersion‑decay model (1‑D semi‑infinite domain, constant water flux, homogeneous porous medium) is formulated with a novel decay entropy metric – defined as the Shannon entropy of the radionuclide age distribution at depth . The intervention (step reduction of surface source by fraction at yields a time‑integrated efficacy , where is the instantaneous relative concentration reduction. Using the Green’s function solution for a flux boundary and the age probability density (with ), we prove that . For fixed mean age, the integral decreases monotonically with increasing entropy . Consequently: where depends on . This predicts higher efficacy at greater depth because broader age distributions (higher ) increase the fraction of radionuclides with ages – i.e., those already affected by the source reduction. Deeper contamination () is more responsive to surface‑applied interventions (e.g., capping, phytoremediation, chemical injection) than shallower contamination – exactly opposing conventional wisdom. A complete experimental design is provided (Section 2.6): 20 soil cores to 1 m, sectioned every 10 cm; compute from ¹³⁷Cs activity profile (λ = 2.3×10⁻² yr⁻¹); apply surface source‑reduction treatment; monitor dissolved ¹³⁷Cs at 10, 30, 60, 90 cm depth for two years; test positive correlation between and . Negative or null correlation falsifies the model. Two Testable Policy‑Relevant Predictions: (1) Depth‑integrated radionuclide activity is a superior predictor of remediation success than surface activity (2) Decay entropy gradients can zone sites for intervention priority (highest → highest efficacy). A complete, mathematically explicit, falsifiable theoretical framework linking decay entropy to intervention efficacy in unsaturated soils.
SN - 3084-8601
SN - 3084-8490
ER -