发表机构
University of Freiburg（弗赖堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究推导了热力学推断中有限时间、小样本下广义电流偏离概率的非渐近上界，揭示了平衡内外涨落差异，得到逆热力学不确定性关系，构造了小数据下的非渐近置信区间并用于检测细致平衡破缺。
AI 中文摘要
我们推导了非渐近上界，针对任意时长观测的几何遍历扩散过程的广义电流，或任意样本量下其样本均值，偏离平稳均值超过给定值的概率。广义电流的测度集中行为由 underlying 动力学的弛豫时间、局部观测的耗散率以及可观测量的固有局部涨落普遍决定。我们揭示了热力学平衡内外涨落的显著定性与定量差异。我们进一步得到了精细的逆热力学不确定性关系，从上方界定广义电流的方差。我们构造了非渐近置信区间，以控制来自小数据（即短轨迹与小样本）的热力学推断中的不确定性，并针对轨迹何时足够长、样本何时足够大给出了首个定量答案。作为示例，我们将结果应用于平衡内外二维Ornstein-Uhlenbeck过程上观测到的电流，展示其如何被用于严格检测细致平衡的破缺。
英文摘要
We derive nonasymptotic upper bounds on the probability that a generalized current of a geometrically ergodic diffusion observed for any amount of time, or its sample mean over any arbitrary sample size, deviates from the stationary mean by more than any given amount. The concentration-of-measure behavior of generalized currents is universally governed by the relaxation time of the underlying dynamics, the locally observed dissipation rate, and the intrinsic local fluctuations of the observable. We uncover stark qualitative and quantitative differences in fluctuations in and out of thermodynamic equilibrium. We further obtain refined inverse thermodynamic uncertainty relations, bounding the variance of generalized currents from above. We construct nonasymptotic confidence intervals for controlling uncertainty in thermodynamic inference from small data, i.e., from short trajectories and small samples, and provide the first quantitative answer to when a trajectory is sufficiently long and a sample is sufficiently large. As an illustration, we apply our results to currents observed on a two-dimensional Ornstein-Uhlenbeck process in and out of equilibrium and show how they can be used to rigorously detect broken detailed balance.
