发表机构
EDHEC Business School（法国北方高等商学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在量子力学中基于记录描述内部时间，通过特定条件设定实现，累积时钟有相关特性，记录有分级标准，还阐明了多时钟问题，包括不同情境下的条件等价关系。
AI 中文摘要
我们在量子力学中建立了基于记录的内部时间描述，稳定记录的形成表示为基于已实现信息的条件设定，沿历史累积的记录代数按包含关系排序。若已实现结果的持续时间仅取决于其条件玻恩概率，在序列条件下具有加和性、连续性且可校准，那么每个结果的实现贡献一个等于其惊奇值（该概率的负对数）的内部持续时间。累积时钟的系综均值是记录过程的香农熵，其矩生成函数由雷尼熵谱确定，实现的时钟可进行杜布分解。记录由可区分性、退相干和稳定性的分级标准表征。我们还阐明了多时钟问题。
英文摘要
We develop a record-based account of internal time in quantum mechanics. Persistent records first define an ordinal chronology through inclusion of their accumulated Boolean algebras. On a specified record filtration, we prove that, under three minimal consistency requirements, namely dependence only on conditional Born weight, invariance under sequential refinement of the same recorded fact, and continuity, the actualization of each outcome contributes an internal time proportional to its \textit{surprisal}, defined as the negative logarithm of that probability. A certain outcome therefore contributes no duration, whereas less probable outcomes contribute larger increments. The mean and variance of the accumulated clock are governed by the Shannon entropy and varentropy of the record process, its moment-generating function is related to the R'enyi entropy spectrum, and its pathwise fluctuations admit a Doob decomposition into a predictable entropic compensator and a martingale. Two further results provide independent consistency checks. Within the stated class of finite-dimensional bipartite states, universal additivity of local clock readings across all admissible local record contexts is equivalent to the absence of entanglement. In the quantum Zeno regime, the number of monitoring rounds may diverge while the expected accumulated surprisal tends to zero. The construction therefore supplies a canonical internal-time functional for a specified quantum record process without presupposing an external clock. It does not by itself identify which physical record processes constitute material clocks; determining their production rates and dynamical realization remains a separate problem.
Comments17 pages, no figure
