ensemble average

简明释义

总集平均

英英释义

例句

1.In quantum mechanics, the ensemble average 集体平均 is crucial for understanding the behavior of particles in a system.

在量子力学中，集体平均 ensemble average 对于理解系统中粒子的行为至关重要。

2.In statistical mechanics, the ensemble average 集体平均 is used to describe the average properties of a system in thermal equilibrium.

在统计力学中，集体平均 ensemble average 用于描述热平衡状态下系统的平均性质。

3.When analyzing weather patterns, meteorologists often rely on the ensemble average 集体平均 from multiple models to make forecasts.

在分析天气模式时，气象学家通常依赖多个模型的 集体平均 ensemble average 来进行预测。

4.The ensemble average 集体平均 of a large number of measurements helps to reduce random errors in experimental data.

大量测量的 集体平均 ensemble average 有助于减少实验数据中的随机误差。

5.The ensemble average 集体平均 of stock prices over a year can provide insights into market trends.

一年内股票价格的 集体平均 ensemble average 可以提供市场趋势的见解。

作文

In the realm of statistical mechanics and thermodynamics, the concept of ensemble average plays a crucial role in understanding the behavior of large systems composed of many particles. An ensemble average refers to the average value of a physical quantity calculated over a large number of identical systems, each representing a possible state of the system under consideration. This concept is fundamental because it allows scientists to make predictions about macroscopic properties based on microscopic behaviors, which can often be chaotic and unpredictable.To illustrate this idea, consider a gas contained in a box. Each molecule of gas moves randomly, colliding with other molecules and the walls of the container. If we want to know the average energy of the gas molecules, we cannot simply observe one molecule and assume its energy represents the entire system. Instead, we need to measure the energy of many molecules and then calculate the ensemble average of these measurements. This ensemble average gives us a more accurate representation of the gas's overall energy, as it accounts for the variations among individual molecules.The importance of the ensemble average extends beyond physics into other fields such as economics, biology, and social sciences. For instance, in economics, researchers might study consumer behavior by examining a large population of individuals. By calculating the ensemble average of spending habits, they can gain insights into general trends and make predictions about future market behavior. Similarly, in biology, the ensemble average can be used to analyze the traits of a population of organisms, helping scientists understand evolutionary processes.One of the key advantages of using the ensemble average is that it smooths out random fluctuations that might occur in smaller samples. In any given moment, the behavior of individual particles or entities can be highly variable. However, when we look at a large ensemble, the random variations tend to cancel each other out, leading to a more stable and reliable average. This property is particularly useful in experimental settings where measuring every single entity is impractical or impossible.Despite its usefulness, the ensemble average does have limitations. It assumes that all systems being averaged are identical and that they are in thermal equilibrium. In cases where systems are not identical or are influenced by external factors, the ensemble average may not provide an accurate representation of the system's behavior. Researchers must be cautious when applying this concept and ensure that the conditions for its validity are met.In conclusion, the ensemble average is a powerful tool for analyzing complex systems across various scientific disciplines. By averaging over a large number of identical systems, we can gain valuable insights into the macroscopic properties of those systems. Whether in physics, economics, or biology, the ensemble average helps us to simplify and understand the underlying patterns that govern the behavior of large groups. As we continue to explore the intricacies of our world, the concept of the ensemble average will remain an essential component of our analytical toolkit, guiding us toward a deeper understanding of the phenomena we observe.

在统计力学和热力学的领域中，ensemble average（集合平均）的概念在理解由众多粒子组成的大系统的行为中起着至关重要的作用。ensemble average指的是对大量相同系统计算的物理量的平均值，每个系统代表了所考虑系统的一个可能状态。这个概念是基础性的，因为它允许科学家根据微观行为做出关于宏观属性的预测，而微观行为往往是混乱和不可预测的。为了说明这一点，考虑一个装有气体的箱子。每个气体分子都是随机运动的，彼此碰撞以及与容器的壁面碰撞。如果我们想知道气体分子的平均能量，我们不能仅仅观察一个分子并假设其能量代表整个系统。相反，我们需要测量许多分子的能量，然后计算这些测量的ensemble average。这个ensemble average为我们提供了气体整体能量的更准确表示，因为它考虑了个别分子之间的变化。ensemble average的重要性超越了物理学，延伸到经济学、生物学和社会科学等其他领域。例如，在经济学中，研究人员可能通过研究大量个体来研究消费者行为。通过计算消费习惯的ensemble average，他们可以获得一般趋势的见解，并对未来市场行为做出预测。同样，在生物学中，ensemble average可用于分析一群生物的特征，帮助科学家理解进化过程。使用ensemble average的一个关键优点是它平滑了可能出现在较小样本中的随机波动。在任何给定时刻，单个粒子或实体的行为可能高度可变。然而，当我们观察一个大的集合时，随机变化往往会相互抵消，从而导致一个更加稳定和可靠的平均值。这一特性在实验环境中尤其有用，因为在这些环境中，测量每个单独实体是不切实际或不可能的。尽管ensemble average非常有用，但它也有局限性。它假设所有被平均的系统是相同的，并且处于热平衡状态。在系统不相同或受到外部因素影响的情况下，ensemble average可能无法提供系统行为的准确表示。研究人员在应用这一概念时必须谨慎，确保满足其有效性的条件。总之，ensemble average是分析各种科学学科中复杂系统的强大工具。通过对大量相同系统进行平均，我们可以获得对这些系统宏观属性的宝贵见解。无论是在物理学、经济学还是生物学中，ensemble average都帮助我们简化并理解支配大群体行为的基本模式。随着我们继续探索世界的复杂性，ensemble average的概念将仍然是我们分析工具包中的一个重要组成部分，引导我们深入理解我们观察到的现象。