ergodic hypothesis

简明释义

遍历假设

英英释义

例句

1.Researchers often test the ergodic hypothesis 遍历假设 in chaotic systems to determine if time averages equal ensemble averages.

研究人员通常在混沌系统中测试 ergodic hypothesis 遍历假设 以确定时间平均值是否等于集合平均值。

2.Understanding the implications of the ergodic hypothesis 遍历假设 can help in predicting the behavior of complex networks.

理解 ergodic hypothesis 遍历假设 的含义有助于预测复杂网络的行为。

3.In statistical mechanics, the validity of the ergodic hypothesis 遍历假设 is crucial for connecting microscopic properties to macroscopic observations.

在统计力学中，ergodic hypothesis 遍历假设 的有效性对于将微观性质与宏观观察联系起来至关重要。

4.The ergodic hypothesis 遍历假设 suggests that over a long period, a system will explore all accessible states.

该 ergodic hypothesis 遍历假设 表明，在长时间内，一个系统将探索所有可接触的状态。

5.In finance, the ergodic hypothesis 遍历假设 can be applied to model the long-term behavior of asset prices.

在金融领域，ergodic hypothesis 遍历假设 可用于模拟资产价格的长期行为。

作文

The concept of the ergodic hypothesis is a fundamental principle in statistical mechanics and thermodynamics that posits that, over a long period of time, a system will explore all accessible microstates uniformly. This idea is crucial for understanding how macroscopic properties emerge from microscopic behavior. To grasp the implications of the ergodic hypothesis, we must first delve into the nature of dynamical systems and the role of time in their evolution.In essence, the ergodic hypothesis suggests that the time average of a system's properties will equal the ensemble average, provided that the system is ergodic. This means that if we observe a system for a sufficiently long time, the different states it occupies will reflect all possible configurations, allowing us to make predictions about its behavior based on statistical averages. This has profound implications in physics, particularly in areas such as thermodynamics, where it helps explain why systems tend to evolve towards equilibrium.To illustrate this concept, consider a simple example of gas particles in a container. According to the ergodic hypothesis, if we were to track the position and velocity of each particle over a long duration, we would find that every particle eventually visits every region of the container. This uniform exploration of phase space leads to the conclusion that, at equilibrium, the macroscopic properties of the gas—such as pressure and temperature—are well-defined and can be described by statistical laws.However, the ergodic hypothesis is not universally applicable. Some systems exhibit behavior that is non-ergodic, meaning they do not explore their phase space uniformly over time. For instance, certain disordered systems or those with strong correlations may become trapped in specific configurations, leading to phenomena such as glassy behavior. Understanding the limitations of the ergodic hypothesis is essential for accurately modeling complex systems in various fields, including condensed matter physics and cosmology.Moreover, the ergodic hypothesis has implications beyond physical sciences; it also finds relevance in fields like economics and biology. In economics, for example, the behaviors of markets can sometimes be analyzed through the lens of ergodicity, suggesting that historical data can inform future trends under certain conditions. Similarly, in biological systems, the dynamics of populations may exhibit ergodic behavior, allowing researchers to predict population distributions over time.In conclusion, the ergodic hypothesis serves as a cornerstone for understanding the relationship between microscopic dynamics and macroscopic phenomena. It provides a framework for predicting system behavior based on statistical principles, although it is essential to acknowledge its limitations. By recognizing both the power and the constraints of the ergodic hypothesis, scientists can better navigate the complexities of the natural world, enhancing our understanding of everything from fundamental physics to intricate biological systems. As we continue to explore the universe, the insights gleaned from the ergodic hypothesis will undoubtedly play a pivotal role in shaping our comprehension of reality.

遍历假设是统计力学和热力学中的一个基本原则，它假设一个系统在长时间内将均匀地探索所有可达的微观状态。这个思想对于理解宏观性质如何从微观行为中涌现至关重要。要掌握遍历假设的影响，我们首先必须深入研究动力系统的性质以及时间在其演变中的作用。本质上，遍历假设表明，如果一个系统是遍历的，那么系统属性的时间平均值将等于集合平均值。这意味着如果我们足够长时间地观察一个系统，它所占据的不同状态将反映所有可能的配置，从而使我们能够基于统计平均值对其行为进行预测。这在物理学中具有深远的意义，特别是在热力学领域，它帮助解释系统为何趋向于平衡。为了说明这个概念，考虑一个简单的例子：容器中的气体粒子。根据遍历假设，如果我们跟踪每个粒子的位置和速度，经过一段较长的时间，我们会发现每个粒子最终会访问容器的每个区域。这种相空间的均匀探索导致了这样的结论：在平衡时，气体的宏观性质——如压力和温度——是明确的，并且可以通过统计规律来描述。然而，遍历假设并不普遍适用。有些系统表现出非遍历行为，这意味着它们不会在时间上均匀地探索其相空间。例如，某些无序系统或具有强相关性的系统可能会被困在特定配置中，导致玻璃态行为等现象。理解遍历假设的局限性对于准确建模各种领域的复杂系统至关重要，包括凝聚态物理和宇宙学。此外，遍历假设不仅在物理科学中具有重要意义；它还在经济学和生物学等领域中找到相关性。例如，在经济学中，市场行为有时可以通过遍历性来分析，暗示历史数据在某些条件下能够为未来趋势提供信息。同样，在生物系统中，种群的动态可能表现出遍历行为，使研究人员能够预测种群随时间变化的分布。总之，遍历假设作为理解微观动态与宏观现象之间关系的基石，为基于统计原则预测系统行为提供了框架，尽管必须承认其局限性。通过认识到遍历假设的力量和约束，科学家们可以更好地应对自然界的复杂性，增强我们对从基础物理到复杂生物系统的理解。随着我们继续探索宇宙，从遍历假设中获得的见解无疑将在塑造我们对现实的理解方面发挥关键作用。