Difference equations of average entropies

2026-08-27

AI Summary

本文通过将熵量嵌入满足Toda型晶格方程的tau函数中，提出了一种基于可积系统的新方法来研究随机态系综的纠缠熵精确矩问题。

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.

Problem

• difference equations
• average entropies
• random state ensembles
• integrable systems
• Toda-type lattice equations

Innovation

• integrable systems
• difference equations
• Toda-type lattice equations
• tau functions