具有状态依赖扩散系数的最概然路径的分辨率依赖性
Resolution dependence of most probable pathways with state-dependent diffusivity
AI总结：
该研究针对具有状态依赖扩散系数的双稳势系统，发现最概然路径随时空管分辨率定性变化，高分辨率下存活概率仅由扩散决定，还推广了Onsager-Machlup作用量并揭示了存活概率比的奇异特性。
摘要：
近期实验通过观测时空内半径为$R$的管状区域内的存活概率，探究了随机系统中轨迹的相对可能性。本文测量了波纹通道中胶体粒子的此类概率，该系统对应具有状态依赖扩散系数的双稳势。与此前针对状态无关噪声的研究结果相反，我们发现最概然路径会随着管半径$R$的改变发生定性变化。我们通过计算过阻尼Langevin动力学预测的存活概率对此进行了解释。在足够高的分辨率（足够小的$R$）下，存活概率仅取决于扩散系数的变化，与确定性力无关；有限$R$修正给出了Onsager-Machlup作用量的推广形式。作为推论，当$R \to 0$时存活概率的比值是奇异的，仅在状态无关噪声的特殊情况下，该比值才会变得正则，并由经典Onsager-Machlup作用量描述。
英文摘要：
Recent experiments have probed the relative likelihoods of trajectories in stochastic systems by observing survival probabilities within a tube of radius $R$ in spacetime. We measure such probabilities here for a colloidal particle in a corrugated channel, corresponding to a bistable potential with state-dependent diffusivity. In contrast to previous findings for state-independent noise, we find that the most probable pathway changes qualitatively as the tube radius $R$ is altered. We explain this by computing the survival probabilities predicted by overdamped Langevin dynamics. At high enough resolution (small enough $R$), survival probabilities depend solely on diffusivity variations, independent of deterministic forces; finite $R$ corrections yield a generalization of the Onsager-Machlup action. As corollary, ratios of survival probabilities are singular as $R \to 0$, but become regular, and described by the classical Onsager-Machlup action, only in the special case of state-independent noise.
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