发表机构
USMBA（穆莱伊斯梅尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非线性效率涨落，提出用Barankin多点界替代线性响应Cramér-Rao界，在有限微扰下恢复方差，增益达1.25-1.57倍，并给出短窗口极限与推断不可行性。
AI 中文摘要
热力学不确定性关系限制了时间反对称电流的涨落。随机效率并非此类量：它是两个奇数量之比，在路径反转下为偶量，且对于常规比值$-W/Q_h$，其矩不存在。我们研究火用比$\u03b7=W/(W+T_0S)$，其矩存在，并探讨在线性响应无法胜任时，动力学有限微扰能认证其方差的多大部分。该问题针对非线性可观测量具有特殊性：对于每个电流，以及每个在转移计数和停留时间上为线性的可观测量，多参数Cramér-Rao界在速率和位点微扰下已等于方差。但对于$\u03b7$并非如此。Cramér-Rao界在微扰方向的超平面上消失，而Barankin多点界应用于倾斜路径测度时在该处保持正值，并在一个三态马达模型中恢复了$\u03b7$方差的75%，而该模型中所有线性响应界均为零。倾斜马尔可夫跳跃路径测度的Gram矩阵是Feynman-Kac矩阵指数，其势为跳跃强度的Hellinger被积函数，微扰的代价是其$\u03c7^2$散度，该散度不受任何耗散界控制。该界捕获了最佳线性响应界的1.25至1.57倍，且增益在多达十六个状态的网络上持续存在。对于Ornstein-Uhlenbeck过程，该构造可精确求解：最优倾斜随$T^{-1/2}$缩放，三个测试点几乎达到上确界。确立了两个极限：增益是短窗口效应，当计数变为高斯时消失；且该界无法转化为推断：粗粒度测量仅从下方界定$\u03c7^2$。该构造是针对手头模型的计算工具，而非不确定性关系。
英文摘要
Thermodynamic uncertainty relations bound the fluctuations of time-antisymmetric currents. Stochastic efficiency is not one: a ratio of two odd quantities, it is even under path reversal, and for the conventional ratio $-W/Q_h$ no moment exists. We work with the exergetic ratio $η=W/(W+T_0S)$, whose moments exist, and ask how much of its variance a finite perturbation of the dynamics can certify when linear response cannot. The question is specific to nonlinear observables: for every current, and every observable linear in transition counts and residence times, the multiparameter Cramér-Rao bound over rate and site perturbations already equals the variance. For $η$ it does not. The Cramér-Rao bound vanishes on a hyperplane of perturbation directions, while the Barankin multi-point bound, applied to tilted path measures, stays positive there and recovers 75% of the variance of $η$ in a three-state motor model where every linear-response bound is zero. The Gram matrix of tilted Markov-jump path measures is a Feynman-Kac matrix exponential whose potential is the Hellinger integrand of the jump intensities, and the cost of a perturbation is its $χ^2$ divergence, which no dissipation bound controls. The bound captures 1.25-1.57 times the best linear-response bound, and the gain persists on networks of up to sixteen states. For an Ornstein-Uhlenbeck process the construction is exactly solvable: the optimal tilt scales as $T^{-1/2}$ and three test points nearly reach the supremum. Two limits are established. The gain is a short-window effect that disappears as the counts become Gaussian, and the bound cannot be turned into inference: coarse measurements bound $χ^2$ only from below. The construction is a computational instrument for a model in hand, not an uncertainty relation.
Comments28 pages, 2 figures, 13 tables. Replication package: https://doi.org/10.5281/zenodo.23042372
