n.各态历经性；遍历性

The concept of ergodicity is crucial in understanding the long-term behavior of stochastic processes, ensuring that time averages equal ensemble averages."
** ergodic性在理解随机过程的长期行为中至关重要，它确保了时间平均值等于集合平均值。**
In physics, ergodic systems explore how a system's microstates visit all accessible configurations over time."
**在物理学中，遍历系统研究系统如何随时间访问所有可到达的微观状态。**
Ergodic theory helps economists model economic systems where each agent's choices, over time, represent the full range of possibilities."
**遍历理论帮助经济学家建模经济系统，其中每位代理随时间的选择代表了所有可能情况的范围。**
A Markov chain is said to be ergodic if it has a unique stationary distribution and eventually reaches it from any starting state."
**如果马尔可夫链有一个唯一的平稳分布，并且从任何初始状态最终都能达到它，那么这个马尔可夫链被称为遍历的。**
Ergodicity in statistical mechanics implies that, given enough time, a system will spend equal time in all its accessible microstates."
**统计力学中的遍历性意味着，给定足够的时间，系统将在所有可访问的微观状态中花费相等的时间。**
The ergodic hypothesis suggests that in thermodynamics, a system's macroscopic properties can be derived from the average behavior of its individual particles over time."
**遍历假设提出，在热力学中，系统的宏观性质可以从其个体粒子随时间的平均行为中推导出来。**
For a dynamical system to be ergodic, it must be possible to observe its entire state space through time evolution."
**对于一个动态系统来说，要成为遍历的，必须能够通过时间演化观察到它的整个状态空间。**
In finance, ergodic models are used to analyze the long-term risk and return of investments, assuming market conditions visit all states equally."
**在金融领域，遍历模型被用来分析投资的长期风险和回报，假设市场条件平等地访问所有状态。**
An ergodic process in signal processing ensures that the statistical properties of a signal remain constant over time."
**在信号处理中，遍历过程确保信号的统计特性随时间保持不变。**
The study of ergodicity is fundamental in understanding complex systems where the behavior over an infinite time horizon is of interest."
**研究遍历性对于理解那些对无限时间跨度内行为感兴趣的复杂系统是基础性的。**