发表机构
University of North Carolina-Chapel Hill（北卡罗来纳大学教堂山分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对依赖历史的非马尔可夫跳跃过程，构建轨迹水平的波动-响应理论，推导精确有限时间/频率关系等，为记忆系统的响应特性提供量化分析框架。
AI 中文摘要
现代实验常将非平衡动力学记录为离散事件序列，其速率依赖于已实现的过去。我们直接基于观测到的事件记录，为这类非马尔可夫跳跃过程建立了波动-响应理论。记忆会破坏状态概率的闭合主方程，但每个跃迁计数仍遵循精确的随机方程。在减去依赖历史的平均事件倾向后，剩余的随机增量是鞅增量——即无法从过去预测的事件部分。不同跃迁及不同时间对应的鞅增量相互正交，这些增量构成了基于记录测量的任意可观测量（如电流、占据时间或事件计数）随机偏差的完整正交基。给定增量的系数是事件后果核，它衡量在已实现的特定历史下，该事件相对于不发生该事件时如何改变对最终可观测量的预测。将该核乘以事件强度，即可得到对应跃迁速率受扰动时的历史条件响应。因此，强度归一化的响应恰好是该事件在可观测量波动中的展开系数，该识别给出了精确的有限时间和有限频率波动-响应关系。对历史取平均后会留下非负的响应异质性间隙，该间隙衡量同一事件的后果在不同历史间的变化强度，并检验所提出的记忆坐标是否具有响应充分性。有限历史版本可从自发轨迹估计，进一步对对数速率灵敏度进行界定，可得到由动力学活性控制的响应-动力学不确定性关系。
英文摘要
Modern experiments often record nonequilibrium dynamics as sequences of discrete events whose rates depend on the realized past. We develop a fluctuation-response theory for such non-Markovian jump processes directly on the observed event record. Memory can destroy a closed master equation for the state probabilities. Each transition count nevertheless obeys an exact stochastic equation. After the history-dependent mean event tendency is subtracted, the remaining random increment is a martingale increment--the part of the event that cannot be predicted from the past. Martingale increments associated with different transitions and different times are orthogonal. These increments form a complete orthogonal basis for the random deviation of any observable measured from the record, such as a current, occupation time, or event count. The coefficient of a given increment is the event-consequence kernel. It measures how that event changes the predicted final observable, relative to continuing without the event, for the particular history already realized. Multiplying this kernel by the event intensity gives the history-conditioned response to perturbing the corresponding transition rate. Thus, the intensity-normalized response is exactly the expansion coefficient of that event in the observable fluctuation. This identification yields exact finite-time and finite-frequency fluctuation-response relations. Averaging over histories leaves a nonnegative response-heterogeneity gap. The gap measures how strongly the consequence of the same event varies across histories and tests whether a proposed memory coordinate is response-sufficient. Finite-history versions can be estimated from spontaneous trajectories. Bounding the logarithmic rate sensitivity further gives response-kinetic uncertainty relations controlled by dynamical activity.
