partition function

简明释义

配分函数

英英释义

例句

1.The partition function 配分函数 can be used to derive the free energy of a system.

可以使用配分函数 partition function 来推导一个系统的自由能。

2.To find the average energy of a system, we need to compute the partition function 配分函数 first.

要找到系统的平均能量，我们首先需要计算配分函数 partition function。

3.The canonical ensemble relies on the partition function 配分函数 to describe systems in thermal equilibrium.

经典系综依赖于配分函数 partition function 来描述处于热平衡中的系统。

4.In statistical mechanics, the partition function 配分函数 is a central concept used to calculate thermodynamic properties.

在统计力学中，配分函数 partition function 是用于计算热力学性质的核心概念。

5.In quantum mechanics, the partition function 配分函数 helps in understanding the behavior of particles at different energy levels.

在量子力学中，配分函数 partition function 有助于理解粒子在不同能级的行为。

作文

The concept of the partition function is fundamental in statistical mechanics and plays a crucial role in understanding the behavior of systems in thermodynamics. At its core, the partition function serves as a mathematical tool that encapsulates all the possible states of a system and their corresponding energies. By summing over all these states, the partition function provides a comprehensive overview of the system's statistical properties. In statistical mechanics, we often deal with systems that have a large number of particles, where it becomes impractical to track each particle individually. Instead, we rely on the partition function to simplify our calculations. For example, consider a gas in a container. Each molecule can occupy various energy levels, and the partition function helps us calculate macroscopic properties such as temperature, pressure, and volume by relating them to these microscopic states.Mathematically, the partition function is expressed as Z = Σ exp(-E_i/kT), where E_i represents the energy of the i-th state, k is the Boltzmann constant, and T is the absolute temperature. This equation shows that the partition function is a sum over all possible states, weighted by the exponential of their negative energy divided by the product of the Boltzmann constant and temperature. The significance of this formula lies in its ability to relate thermodynamic quantities to statistical properties of the system.One of the most important applications of the partition function is in deriving the Helmholtz free energy (F), which is given by F = -kT ln(Z). This relationship illustrates how the partition function connects microscopic details of a system to its macroscopic thermodynamic behavior. By knowing the partition function, we can easily compute various thermodynamic potentials, thereby gaining insights into phase transitions, chemical reactions, and other phenomena.Furthermore, the partition function is not limited to classical systems; it also extends to quantum systems. In quantum mechanics, the partition function accounts for the discrete energy levels of particles, allowing physicists to analyze systems at very low temperatures where quantum effects become significant. This versatility makes the partition function an essential concept across different fields of physics.In conclusion, the partition function is a powerful concept that bridges the gap between microscopic and macroscopic descriptions of physical systems. Its ability to summarize all possible states and their contributions to the overall behavior of a system makes it indispensable in statistical mechanics and thermodynamics. As we continue to explore complex systems, the partition function will undoubtedly remain a key tool for understanding the underlying principles that govern physical phenomena.

“分区函数”这一概念在统计力学中是基础性的，并在理解热力学系统的行为中发挥着至关重要的作用。从本质上讲，“分区函数”作为一种数学工具，封装了一个系统的所有可能状态及其对应的能量。通过对这些状态进行求和，“分区函数”提供了系统统计特性的全面概述。在统计力学中，我们通常处理具有大量粒子的系统，在这种情况下，逐个跟踪每个粒子变得不切实际。因此，我们依赖“分区函数”来简化我们的计算。例如，考虑一个容器中的气体。每个分子可以占据不同的能量水平，而“分区函数”帮助我们通过将它们与这些微观状态联系起来，计算温度、压力和体积等宏观性质。从数学上讲，“分区函数”表示为 Z = Σ exp(-E_i/kT)，其中 E_i 代表第 i 个状态的能量，k 是玻尔兹曼常数，T 是绝对温度。这个方程表明“分区函数”是对所有可能状态的加和，以它们的负能量除以玻尔兹曼常数和温度的乘积的指数权重。这一公式的重要性在于它能够将热力学量与系统的统计特性联系起来。“分区函数”的一个重要应用是在推导亥姆霍兹自由能（F），其表达式为 F = -kT ln(Z)。这个关系说明了“分区函数”如何将系统的微观细节与其宏观热力学行为相连接。通过了解“分区函数”，我们可以轻松计算各种热力学势，从而深入了解相变、化学反应和其他现象。此外，“分区函数”不仅限于经典系统；它还扩展到量子系统。在量子力学中，“分区函数”考虑了粒子的离散能级，使物理学家能够分析在非常低温下量子效应变得显著的系统。这种多功能性使“分区函数”成为物理学不同领域的重要概念。总之，“分区函数”是一个强大的概念，它架起了物理系统微观描述与宏观描述之间的桥梁。它总结所有可能状态及其对系统整体行为的贡献的能力，使其在统计力学和热力学中不可或缺。随着我们继续探索复杂系统，“分区函数”无疑将继续成为理解支配物理现象的基本原理的关键工具。