The rupture of a polymer chain maintained at temperature $T$ under fixed tension is prototypical to a wide array of systems failing under constant external stress and random perturbations. Past research focused on analytic and numerical studies of the mean rate of collapse of such a chain. Surprisingly, an analytic calculation of the probability distribution function (PDF) of collapse rates appears to be lacking. Since rare events of rapid collapse can be important and even catastrophic, we present here a theory of this distribution, with a stress on its tail of fast rates. We show that the tail of the PDF is a power law with a universal exponent that is theoretically determined. Extensive numerics validate the offered theory. Lessons pertaining to other problems of the same type are drawn.

中文翻译：

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张力下聚合物链的老化和破坏

维持温度的聚合物链断裂 $Ť$固定张力下的原型对于在恒定外部应力和随机扰动下失效的各种系统都是典型的。过去的研究集中在这种链的平均崩溃率的分析和数值研究上。令人惊讶的是，似乎缺乏崩溃率概率分布函数（PDF）的解析计算。由于罕见的快速崩溃事件可能很重要甚至是灾难性的，因此我们在这里介绍这种分布的理论，并强调其快速增长的尾巴。我们表明，PDF的尾部是幂定律，具有在理论上确定的通用指数。大量的数字验证了所提供的理论。汲取了与其他同类问题有关的经验教训。