A transition path is a part of a one-dimensional trajectory of a diffusing particle, which starts from point a and is terminated as soon as it comes to point b for the first time. It is the trajectory’s final segment that leaves point a and goes to point b without returning to point a. The duration of this segment is called transition path time or, alternatively, direct transit time. We study the mean transition path time in monotonically increasing entropy potentials of the narrowing cones in spaces of different dimensions. We find that this time, normalized to its value in the absence of the potential, monotonically increases with the barrier height for the entropy potential of a narrowing two-dimensional cone, is independent of the barrier height for a narrowing three-dimensional cone, and monotonically decreases with the barrier height for narrowing cones in spaces of higher dimensions. Moreover, we show that as the barrier height tends to infinity, the normalized mean transition path time approaches its universal limiting value n/3, where n = 2, 3, 4, ... is the space dimension. This is in sharp contrast to the asymptotic behavior of this quantity in the case of a linear potential of mean force, for which it approaches zero in this limit.

中文翻译：

---

熵势中平均跃迁路径时间依赖于势垒高度的特殊性

过渡路径是扩散粒子的一维轨迹的一部分，它从a点开始，第一次到达b点就终止。离开点a并到达点b而不返回点a是轨迹的最后一段. 该段的持续时间称为过渡路径时间，或者直接过渡时间。我们研究了不同维度空间中变窄锥的熵势单调递增的平均过渡路径时间。我们发现，这一次，在没有势的情况下归一化为它的值，随着变窄二维锥的熵势的势垒高度单调增加，与变窄的三维锥的势垒高度无关，并且在更高维度的空间中缩小锥体的势垒高度随势垒高度单调递减。此外，我们表明，随着势垒高度趋于无穷大，归一化平均过渡路径时间接近其通用极限值n /3，其中n= 2, 3, 4, ... 是空间维度。这与该量在平均力的线性势的情况下的渐近行为形成鲜明对比，在该极限中它接近于零。