Initial-Trace Insufficiency and Entropy-Accounting Separation in Finite-Volume Coarse Graining
Abstract
Coarse finite-volume information does not automatically define an exact pathwise closure for the restricted evolution of a fine-grid realization. We study two one-step information boundaries that are distinct from recursive predictive memory. First, we show that parent averages together with complete initial parent-interface trace pairs are sufficient for one forward-Euler finite-volume transition with a deterministic two-state numerical flux, but they do not generally determine a completed second-order strong-stability-preserving Runge-Kutta, equivalently Heun, transition. An explicit scalar upwind collision shows that hidden interior data can affect later stage traces and hence the completed parent update, even when initial traces and parent averages agree. Second, we show that exact conservative one-step closure is not the same as entropy-accounting closure. A parent entropy balance obtained from a cellwise numerical entropy balance contains a subcell Jensen gap, a realized entropy-flux difference, and residual dissipation. For a declared Burgers-Rusanov conservative flux and a declared Rusanov-type numerical entropy flux, we construct a sign-indexed finite family in which all branches have identical parent averages, identical conservative interface registers, and identical next parent averages, while the entropy-interface register distinguishes every branch. Under the uniform branch law, the conservative channel leaves nonzero deterministic squared-error floors for both the raw entropy register and its cyclic divergence. The results give a concise finite-volume information-sufficiency test for multistage interface data and entropy-side accounting.
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BibTeX
@misc{polemitis2026initialtrace,
title = {{Initial-Trace Insufficiency and Entropy-Accounting Separation in Finite-Volume Coarse Graining}},
author = {Antonis Polemitis and Nicholas Christakis and Dimitris Drikakis},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04001},
eprint = {2611.04001},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04001},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Initial-Trace Insufficiency and Entropy-Accounting Separation in Finite-Volume Coarse Graining
AU - Antonis Polemitis
AU - Nicholas Christakis
AU - Dimitris Drikakis
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.04001
UR - https://arxiv.org/abs/2611.04001
AB - Coarse finite-volume information does not automatically define an exact pathwise closure for the restricted evolution of a fine-grid realization. We study two one-step information boundaries that are distinct from recursive predictive memory. First, we show that parent averages together with complete initial parent-interface trace pairs are sufficient for one forward-Euler finite-volume transition with a deterministic two-state numerical flux, but they do not generally determine a completed second-order strong-stability-preserving Runge-Kutta, equivalently Heun, transition. An explicit scalar upwind collision shows that hidden interior data can affect later stage traces and hence the completed parent update, even when initial traces and parent averages agree. Second, we show that exact conservative one-step closure is not the same as entropy-accounting closure. A parent entropy balance obtained from a cellwise numerical entropy balance contains a subcell Jensen gap, a realized entropy-flux difference, and residual dissipation. For a declared Burgers-Rusanov conservative flux and a declared Rusanov-type numerical entropy flux, we construct a sign-indexed finite family in which all branches have identical parent averages, identical conservative interface registers, and identical next parent averages, while the entropy-interface register distinguishes every branch. Under the uniform branch law, the conservative channel leaves nonzero deterministic squared-error floors for both the raw entropy register and its cyclic divergence. The results give a concise finite-volume information-sufficiency test for multistage interface data and entropy-side accounting.
ER -