时间之箭（第二定律）作为大系统的随机驱动涌现特性
The arrow of time (second law) as a randomness-driven emergent property of large systems
摘要：
时间箭头是一种不可逆现象，适用于经历可逆动力学的质点系。从玻尔兹曼时代到今天，时间之箭一直引发争论和研究。然而，纳米技术和相关实验技术的巨大增长带来了时间之箭的前沿，因为它的实际影响。利用一维扩散的质点系的模拟，我们表明，时间箭头是一个大系统的涌现属性。我们表明，一个质点系的重现时间，以返回到其原始配置的增长迅速的粒子数的增长。在模拟的基础上，我们给出了经典粒子、费米子和玻色子的递推时间的表达式。玻色子系统的递归时间最短，而经典粒子系统的递归时间最长。平均重现时间的基本分布是泊松分布的玻色子和高斯分布的费米子和经典粒子。编码动力学的概率方法使测试过程而不是扩散，并量化其对递归时间的影响。
英文摘要：
The arrow of time is an irreversible phenomenon for a system of particles undergoing reversible dynamics. Since the time of Boltzmann to this day, the arrow of time has led to debate and research. However, the enormous growth of nanotechnology and associated experimental techniques has brought the arrow of time at the forefront because of its practical implications. Using simulations of one-dimensional diffusion of a system of particles, we show that the arrow of time is an emergent property of a large system. We show that the recurrence time for a system of particles to return to its original configuration grows rapidly as the number of particles grows. Based on the simulations, we have provided the expressions for recurrence times for classical particles, Fermions, and Bosons. A system of Bosons has the shortest recurrence time, whereas a system of classical particles has the longest recurrence time. The underlying distribution around the mean recurrence time is Poisson-distributed for Bosons and Gaussian-distributed for Fermions and classical particles. The probabilistic approach to encode dynamics enables testing processes other than diffusion and quantify their effects on the recurrence time.
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