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Statistical mechanics is one of the pillars of modern physics. It is necessary for the fundamental study of any physical system that has many degrees of freedom. The approach is based on statistical methods, probability theory and the microscopic physical laws.

Statistical mechanics is one of the pillars of modern physics. It is necessary for the fundamental study of any physical system that has many degrees of freedom. The approach is based on statistical methods, probability theory and the microscopic physical laws.

<font color="#FF8000">统计力学 Statistical mechanics</font>是现代物理学的支柱之一。对于具有多个<font color="#FF8000">自由度 Degrees of Freedom</font>的物理系统的基础研究，统计力学是不可或缺的。统计力学的方法是基于<font color="#FF8000">统计学方法 Statistical Methods</font>、<font color="#FF8000">概率论 Probability Theory</font>和<font color="#FF8000">微观物理定律 Microscopic Physical Laws</font>。

<font color="#FF8000">统计力学 Statistical Mechanics</font>是现代物理学的支柱之一。对于具有多个<font color="#FF8000">自由度 Degrees of Freedom</font>的物理系统的基础研究，统计力学是不可或缺的。统计力学的方法是基于<font color="#FF8000">统计学方法 Statistical Methods</font>、<font color="#FF8000">概率论 Probability Theory</font>和<font color="#FF8000">微观物理定律 Microscopic Physical Laws</font>。

Statistical mechanics can also be used to study systems that are out of equilibrium. An important subbranch known as non-equilibrium statistical mechanics (sometimes called statistical dynamics) deals with the issue of microscopically modelling the speed of irreversible processes that are driven by imbalances. Examples of such processes include chemical reactions or flows of particles and heat. The fluctuation–dissipation theorem is the basic knowledge obtained from applying non-equilibrium statistical mechanics to study the simplest non-equilibrium situation of a steady state current flow in a system of many particles.

Statistical mechanics can also be used to study systems that are out of equilibrium. An important subbranch known as non-equilibrium statistical mechanics (sometimes called statistical dynamics) deals with the issue of microscopically modelling the speed of irreversible processes that are driven by imbalances. Examples of such processes include chemical reactions or flows of particles and heat. The fluctuation–dissipation theorem is the basic knowledge obtained from applying non-equilibrium statistical mechanics to study the simplest non-equilibrium situation of a steady state current flow in a system of many particles.

统计力学也可以用来研究非平衡的系统。<font color="#FF8000">非平衡统计力学 non-equilibrium statistical mechanics</font>(有时称为统计动力学)是统计力学的重要分支，它涉及的问题是对由非平衡导致的不可逆过程的速度进行微观模拟。例如化学反应或粒子流和热流。<font color="#FF8000">涨落-耗散定理 Fluctuation–Dissipation Theorem</font>是人们从非平衡态统计力学中获得的基本知识，它是在应用非平衡态统计力学来研究多粒子系统中稳态电流流动这样的最简单的非平衡态情况下所发现的。

统计力学也可以用来研究非平衡的系统。<font color="#FF8000">非平衡统计力学 Non-equilibrium Statistical Mechanics</font>(有时称为统计动力学)是统计力学的重要分支，它涉及的问题是对由非平衡导致的不可逆过程的速度进行微观模拟。例如化学反应或粒子流和热流。<font color="#FF8000">涨落-耗散定理 Fluctuation–Dissipation Theorem</font>是人们从非平衡态统计力学中获得的基本知识，它是在应用非平衡态统计力学来研究多粒子系统中稳态电流流动这样的最简单的非平衡态情况下所发现的。

There is however a disconnection between these laws and everyday life experiences, as we do not find it necessary (nor even theoretically possible) to know exactly at a microscopic level the simultaneous positions and velocities of each molecule while carrying out processes at the human scale (for example, when performing a chemical reaction). Statistical mechanics fills this disconnection between the laws of mechanics and the practical experience of incomplete knowledge, by adding some uncertainty about which state the system is in.

There is however a disconnection between these laws and everyday life experiences, as we do not find it necessary (nor even theoretically possible) to know exactly at a microscopic level the simultaneous positions and velocities of each molecule while carrying out processes at the human scale (for example, when performing a chemical reaction). Statistical mechanics fills this disconnection between the laws of mechanics and the practical experience of incomplete knowledge, by adding some uncertainty about which state the system is in.

然而，这些定律与日常生活经验之间存在着脱节。因为对于在人类尺度上进行过程(例如化学反应)，我们没有必要(甚至在理论上也不可能)在微观层面上准确地知道每个分子所在的位置及其速度。统计力学通过增加一些对于系统状态的不确定性，填补了力学定律和人类不完全知识的实践经验之间的脱节。

然而，这些定律与日常生活经验之间存在着脱节。因为对于在人类尺度上进行的过程(例如化学反应)，我们没有必要(甚至在理论上也不可能)在微观层面上准确地知道每个分子所在的位置及其速度。统计力学通过增加一些对于系统状态的不确定性，填补了力学定律和人类不完全知识的实践经验之间的脱节。

For an isolated system with an exactly known energy and exactly known composition, the system can be found with equal probability in any microstate consistent with that knowledge.

For an isolated system with an exactly known energy and exactly known composition, the system can be found with equal probability in any microstate consistent with that knowledge.

The equal a priori probability postulate therefore provides a motivation for the [[microcanonical ensemble]] described below. There are various arguments in favour of the equal a priori probability postulate:

The equal a priori probability postulate therefore provides a motivation for the [[microcanonical ensemble]] described below. There are various arguments in favour of the equal a priori probability postulate:

The equal a priori probability postulate therefore provides a motivation for the microcanonical ensemble described below. There are various arguments in favour of the equal a priori probability postulate:

The equal a priori probability postulate therefore provides a motivation for the microcanonical ensemble described below. There are various arguments in favour of the equal a priori probability postulate:

因此，先验概率相等假设为下面描述的<font color="#FF8000">微正则系综 microcanonical ensemble</font>提供了一个动力。有各种各样的论据支持先验概率相等假设:

因此，先验概率相等假设为下面描述的<font color="#FF8000">微正则系综 Microcanonical Ensemble</font>提供了一个动力。有各种各样的论据支持先验概率相等假设:

* [[Ergodic hypothesis]]: An ergodic system is one that evolves over time to explore "all accessible" states: all those with the same energy and composition. In an ergodic system, the microcanonical ensemble is the only possible equilibrium ensemble with fixed energy. This approach has limited applicability, since most systems are not ergodic.

* [[Ergodic hypothesis]]: An ergodic system is one that evolves over time to explore "all accessible" states: all those with the same energy and composition. In an ergodic system, the microcanonical ensemble is the only possible equilibrium ensemble with fixed energy. This approach has limited applicability, since most systems are not ergodic.

* and irreversible processes in general.

* and irreversible processes in general.

* [[热传导|材料的内部运动来传导热量]]，由热度不平衡来驱动，

* [[热传导|材料内部的物质运动来传导热量]]，由热度不平衡来驱动，

* [[导电|导体内电荷的运动产生电流]]，由电压不平衡来驱动，

* [[导电|导体内电荷的运动产生电流]]，由电压不平衡来驱动，