Spectral Model Links Boundary Geometry to Power-Law Decay in Transport Systems
Researchers have developed a first-principles spectral mechanism that explains how power-law relaxation and nonextensive q-exponential decay emerge in non-ideal transport systems. The model treats an incompletely mixed reactor as a layered diffusion matrix with an absorbing boundary, showing that heavy-tailed behavior arises from the geometric interaction between initial tracer placement and boundary configuration. The work establishes a direct mathematical link between linear diffusion transport and nonextensive statistical mechanics, potentially clarifying a long-standing question about the physical origins of anomalous relaxation in natural and engineered systems.
A new theoretical study posted to arXiv derives, from first principles, how power-law tails and q-exponential decay functions — hallmarks of nonextensive statistical mechanics — can emerge from ordinary linear diffusion in geometrically constrained systems. By modeling an incompletely mixed reactor as a layered diffusion matrix with an absorbing boundary, the authors show that macroscopic power-law behavior depends critically on how the initial tracer concentration profile projects onto low-wavenumber eigenmodes of the system, generating an emergent Gamma distribution of relaxation rates. In the one-dimensional case with a volumetrically distributed asymmetric initial profile and infinitesimally thin boundary layer, the model reproduces the nonextensive q-exponential decay exactly across the full temporal domain, with a specific exponent of q = 5/3. Extended to d dimensions with a highly localized, boundary-adjacent initial condition, the scaling exponents and q values vary with spatial boundary configuration — but notably, in the one-dimensional limit these distinct formulations converge, making the q = 5/3 exponent geometrically invariant. The study bridges linear transport theory and Tsallis nonextensive statistics, suggesting that anomalous heavy-tailed relaxation observed in many physical and engineered systems may be fully explainable by boundary geometry and spectral dimensionality rather than requiring exotic microscopic assumptions.
What's missing
As a theoretical preprint, the study has not yet undergone peer review. The authors do not report experimental validation of the model against empirical data from real natural or engineered systems, leaving open the question of how well the idealized geometric assumptions hold in practice. The range of physical systems to which the q = 5/3 invariance result applies is not explicitly bounded.
What different sources said
- arXiv physicsCenter
Universal Theory of Decaying Turbulence
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