canonical ensemble

简明释义

正则系综

英英释义

例句

1.To calculate the average energy of a system in a canonical ensemble, one must consider all possible microstates.

要计算规范系综中系统的平均能量，必须考虑所有可能的微观状态。

2.The canonical ensemble can be used to derive thermodynamic properties of systems at equilibrium.

规范系综可用于推导处于平衡状态的系统的热力学性质。

3.The partition function is a key concept when analyzing a canonical ensemble.

在分析规范系综时，配分函数是一个关键概念。

4.In statistical mechanics, a canonical ensemble refers to a system in thermal equilibrium with a heat bath at a fixed temperature.

在统计力学中，规范系综指的是与固定温度的热库处于热平衡的系统。

5.In a canonical ensemble, the number of particles and volume are fixed while the temperature is variable.

在规范系综中，粒子数和体积是固定的，而温度是可变的。

作文

In statistical mechanics, the concept of a canonical ensemble is fundamental for understanding the behavior of systems in thermal equilibrium. A canonical ensemble refers to a collection of systems that are all in contact with a heat reservoir at a fixed temperature. This setup allows us to analyze how particles interact and exchange energy while maintaining a constant temperature, which is essential for many physical processes. The significance of the canonical ensemble lies in its ability to simplify complex calculations and provide insights into thermodynamic properties.To delve deeper, let’s consider a simple example: imagine a box filled with gas particles. When these particles collide with each other or the walls of the box, they exchange energy. If we want to study the average energy of these particles at a specific temperature, we can use the canonical ensemble framework. In this scenario, the system is allowed to exchange energy with a larger environment, but the number of particles and the volume remain constant.The mathematical foundation of the canonical ensemble is based on the Boltzmann distribution, which describes the probability of a system being in a particular energy state at a given temperature. According to this distribution, the likelihood of finding the system in a state with energy E is proportional to exp(-E/kT), where k is the Boltzmann constant and T is the absolute temperature. This relationship highlights how temperature influences the distribution of energy among the particles in the system. One of the key applications of the canonical ensemble is in calculating macroscopic properties such as pressure, volume, and temperature. By averaging over all possible microstates of the system, we can derive equations of state that correlate these macroscopic variables. For instance, the Helmholtz free energy can be obtained from the partition function, which is a crucial component in the canonical ensemble framework. The partition function essentially sums up all the possible states of the system, weighted by their probabilities, allowing us to extract valuable thermodynamic quantities.Moreover, the canonical ensemble provides a powerful tool for studying phase transitions. As the temperature changes, the system may undergo transitions between different phases, such as solid, liquid, and gas. By analyzing the behavior of the canonical ensemble near critical points, researchers can gain insights into the nature of these transitions and the underlying mechanisms that drive them.In conclusion, the canonical ensemble is a vital concept in statistical mechanics that enables scientists to understand and predict the behavior of systems in thermal equilibrium. Its applications range from calculating thermodynamic properties to exploring phase transitions. By employing the principles of the canonical ensemble, we can bridge the gap between microscopic interactions and macroscopic observations, ultimately enhancing our comprehension of the physical world around us.

在统计力学中，规范系综的概念对于理解热平衡系统的行为至关重要。规范系综指的是一组与固定温度的热库接触的系统。这种设置使我们能够分析粒子如何相互作用并交换能量，同时保持恒定的温度，这对于许多物理过程是必不可少的。规范系综的重要性在于它能够简化复杂的计算，并提供对热力学性质的洞察。为了更深入地理解，我们可以考虑一个简单的例子：想象一个装满气体粒子的盒子。当这些粒子相互碰撞或与盒子的墙壁碰撞时，它们会交换能量。如果我们想研究这些粒子在特定温度下的平均能量，我们可以使用规范系综框架。在这个场景中，系统被允许与更大的环境交换能量，但粒子的数量和体积保持不变。规范系综的数学基础是基于玻尔兹曼分布，该分布描述了在给定温度下系统处于特定能量状态的概率。根据这个分布，系统处于能量E状态的可能性与exp(-E/kT)成正比，其中k是玻尔兹曼常数，T是绝对温度。这个关系突显了温度如何影响系统中粒子之间能量的分布。规范系综的一个关键应用是在计算宏观性质（如压力、体积和温度）方面。通过对系统所有可能的微观状态进行平均，我们可以推导出将这些宏观变量关联起来的状态方程。例如，自由能可以从配分函数中获得，而配分函数是规范系综框架中的一个关键组成部分。配分函数本质上对系统所有可能状态进行加权求和，从而使我们能够提取出有价值的热力学量。此外，规范系综为研究相变提供了强大的工具。随着温度的变化，系统可能经历不同相之间的转变，例如固体、液体和气体。通过分析规范系综在临界点附近的行为，研究人员可以深入了解这些转变的性质及其驱动机制。总之，规范系综是统计力学中的一个重要概念，使科学家能够理解和预测热平衡系统的行为。它的应用范围从计算热力学性质到探索相变。通过采用规范系综的原则，我们可以弥合微观相互作用与宏观观察之间的差距，最终增强我们对周围物理世界的理解。