AI 中文总结
研究条件控制的热力学几何，发现霍列沃信息等信息量不能唯一确定条件控制的热力学值，缺失的是被动谱重排向量，其与哈密顿量能隙结构的几何配对确定条件控制优势，揭示了相关几何并明确了最小操作描述符。
AI 中文摘要
信息被广泛视为条件控制带来热力学优势的基础资源。然而，我们发现诸如霍列沃信息和可区分性等信息量虽限制了可实现的优势，但并不能唯一确定其热力学值。缺失的要素是一个被动谱重排向量，它表征了条件对系综的影响。具体而言，条件控制优势由该向量与哈密顿量能隙结构之间的几何配对精确确定。此结果揭示了条件控制的热力学几何，解释了信息等效系综为何能具有不同热力学值，并确定被动谱重排向量是确定固定哈密顿量条件控制热力学值所需的最小操作描述符。
英文摘要
Information is widely regarded as the resource underlying the thermodynamic advantages enabled by conditional control. We show, however, that informational quantities such as Holevo information and accessible distinguishability, although constraining the achievable advantage, do not uniquely determine its thermodynamic value. The missing ingredient is a passive spectral rearrangement vector that characterizes the effect of conditioning on the ensemble. Specifically, the conditional-control advantage is exactly determined by the geometric pairing between this vector and the Hamiltonian energy-gap structure. This result reveals a thermodynamic geometry of conditional control, explains how informationally equivalent ensembles can possess different thermodynamic values, and identifies the passive spectral rearrangement vector as the minimal operational descriptor required to determine the thermodynamic value of conditional control for a fixed Hamiltonian.
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