Difference equations of average entropies
Abstract
Exact cumulants of entanglement entropies of random state ensembles have traditionally been studied within the random matrix framework. In this work, we propose an alternative approach based on the intrinsic connection to integrable systems. The central idea is to embed entropic quantities into tau functions satisfying Toda-type lattice equations, which in turn yield linear difference equations for their averages. Directly solving the difference equations recovers exact entropy formulas in the literature. The integrable systems approach bypasses the case-by-case, ensemble-dependent derivations required by random matrix methods. The approach also suggests a possible route towards unified and more efficient higher-order cumulant calculations by exploring integrable hierarchies.
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BibTeX
@misc{huang2026difference,
title = {{Difference equations of average entropies}},
author = {Youyi Huang and Linfeng Wei and Lu Wei and Peter J. Forrester},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27829},
eprint = {2608.27829},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27829},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Difference equations of average entropies
AU - Youyi Huang
AU - Linfeng Wei
AU - Lu Wei
AU - Peter J. Forrester
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.27829
UR - https://arxiv.org/abs/2608.27829
AB - Exact cumulants of entanglement entropies of random state ensembles have traditionally been studied within the random matrix framework. In this work, we propose an alternative approach based on the intrinsic connection to integrable systems. The central idea is to embed entropic quantities into tau functions satisfying Toda-type lattice equations, which in turn yield linear difference equations for their averages. Directly solving the difference equations recovers exact entropy formulas in the literature. The integrable systems approach bypasses the case-by-case, ensemble-dependent derivations required by random matrix methods. The approach also suggests a possible route towards unified and more efficient higher-order cumulant calculations by exploring integrable hierarchies.
ER -