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{{Short description|Physics of large number of particles' statistical behavior}}

{{Short description|Physics of large number of particles' statistical behavior}}

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="#FFD700">统计力学</font>是现代物理学的支柱之一，对于任何具有多个自由度的物理系统的基础研究都很必要。统计力学的基础是统计学方法、概率论和微观物理定律。

<font color="#FF8000">统计力学 Statistical mechanics</font>是现代物理学的支柱之一，对于任何具有多个自由度的物理系统的基础研究都很必要。统计力学的基础是统计学方法、概率论和微观物理定律。

It can be used to explain the thermodynamic behaviour of large systems. This branch of statistical mechanics, which treats and extends classical thermodynamics, is known as statistical thermodynamics or equilibrium statistical mechanics.

It can be used to explain the thermodynamic behaviour of large systems. This branch of statistical mechanics, which treats and extends classical thermodynamics, is known as statistical thermodynamics or equilibrium statistical mechanics.

统计力学可以用来解释大系统的热力学行为，其中一个分支处理和扩展了经典热力学，被称为<font color="#FFD700">统计热力学</font>或<font color="#FFD700">平衡态统计力学</font>。

统计力学可以用来解释大系统的热力学行为，其中一个分支处理和扩展了经典热力学，被称为<font color="#FF8000">统计热力学 statistical thermodynamics</font>或<font color="#FF8000">平衡态统计力学 equilibrium statistical mechanics</font>。

Statistical mechanics describes how macroscopic observations (such as temperature and pressure) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as heat capacity) to microscopic behavior, whereas, in classical thermodynamics, the only available option would be to measure and tabulate such quantities for various materials.

Statistical mechanics describes how macroscopic observations (such as temperature and pressure) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as heat capacity) to microscopic behavior, whereas, in classical thermodynamics, the only available option would be to measure and tabulate such quantities for various materials.

统计力学描述了宏观观测量(如温度和压强)与围绕平均值波动的微观参数的关系。它将热力学量(比如<font color="#FFD700">热容</font>)与微观行为联系起来，而在经典热力学中，唯一可行的选择就是测量和列出各种材料的热力学量。

统计力学描述了宏观观测量(如温度和压强)与围绕平均值波动的微观参数的关系。它将热力学量(比如<font color="#FF8000">热容 heat capacity</font>)与微观行为联系起来，而在经典热力学中，唯一可行的选择就是测量和列出各种材料的热力学量。

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="#FFD700">非平衡统计力学</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="#FFD700">涨落-耗散定理</font>是人们从非平衡态统计力学中获得的基本知识，这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，这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。

{{main|Mechanics|Statistical ensemble (mathematical physics)|l2=Statistical ensemble}}

{{main|Mechanics|Statistical ensemble (mathematical physics)|l2=Statistical ensemble}}

原理：力学和<font color="#FFD700">系综</font>

原理：力学和<font color="#FF8000">系综 ensembles</font>

In physics, two types of mechanics are usually examined: [[classical mechanics]] and [[quantum mechanics]]. For both types of mechanics, the standard mathematical approach is to consider two concepts:

In physics, two types of mechanics are usually examined: [[classical mechanics]] and [[quantum mechanics]]. For both types of mechanics, the standard mathematical approach is to consider two concepts:

In physics, two types of mechanics are usually examined: classical mechanics and quantum mechanics. For both types of mechanics, the standard mathematical approach is to consider two concepts:

In physics, two types of mechanics are usually examined: classical mechanics and quantum mechanics. For both types of mechanics, the standard mathematical approach is to consider two concepts:

在物理学中，通常有两种力学被研究: <font color="#FFD700">经典力学</font>和<font color="#FFD700">量子力学</font>。对于这两种类型的力学，标准的数学方法是考虑两个概念:

在物理学中，通常有两种力学被研究: <font color="#FF8000">经典力学 classical mechanics</font>和<font color="#FF8000">量子力学 quantum mechanics</font>。对于这两种类型的力学，标准的数学方法是考虑两个概念

# The complete state of the mechanical system at a given time, mathematically encoded as a [[phase space|phase point]] (classical mechanics) or a pure [[quantum state vector]] (quantum mechanics).

# The complete state of the mechanical system at a given time, mathematically encoded as a [[phase space|phase point]] (classical mechanics) or a pure [[quantum state vector]] (quantum mechanics).

  The complete state of the mechanical system at a given time, mathematically encoded as a phase point (classical mechanics) or a pure quantum state vector (quantum mechanics).

  The complete state of the mechanical system at a given time, mathematically encoded as a phase point (classical mechanics) or a pure quantum state vector (quantum mechanics).

力学系统在给定时间内的完整状态，用数学表示为<font color="#FFD700">相空间</font>中的点(经典力学)或纯量子态矢量(量子力学)。

力学系统在给定时间内的完整状态，用数学表示为<font color="#FF8000">相空间 phase space</font>中的点(经典力学)或纯量子态矢量(量子力学)。

# An equation of motion which carries the state forward in time: [[Hamilton's equations]] (classical mechanics) or the [[time-dependent Schrödinger equation]] (quantum mechanics)

# An equation of motion which carries the state forward in time: [[Hamilton's equations]] (classical mechanics) or the [[time-dependent Schrödinger equation]] (quantum mechanics)

  An equation of motion which carries the state forward in time: Hamilton's equations (classical mechanics) or the time-dependent Schrödinger equation (quantum mechanics)

  An equation of motion which carries the state forward in time: Hamilton's equations (classical mechanics) or the time-dependent Schrödinger equation (quantum mechanics)

一个运动方程描述状态在时间上的演化: <font color="#FFD700">哈密尔顿方程</font>(经典力学)或<font color="#FFD700">含时薛定谔方程</font>(量子力学)

一个运动方程描述状态在时间上的演化: <font color="#FF8000">哈密尔顿方程 Hamilton's equations</font>(经典力学)或<font color="#FF8000">含时薛定谔方程 time-dependent Schrödinger equation</font>(量子力学)

Using these two concepts, the state at any other time, past or future, can in principle be calculated.

Using these two concepts, the state at any other time, past or future, can in principle be calculated.

Whereas ordinary mechanics only considers the behaviour of a single state, statistical mechanics introduces the statistical ensemble, which is a large collection of virtual, independent copies of the system in various states. The statistical ensemble is a probability distribution over all possible states of the system. In classical statistical mechanics, the ensemble is a probability distribution over phase points (as opposed to a single phase point in ordinary mechanics), usually represented as a distribution in a phase space with canonical coordinates. In quantum statistical mechanics, the ensemble is a probability distribution over pure states, and can be compactly summarized as a density matrix.

Whereas ordinary mechanics only considers the behaviour of a single state, statistical mechanics introduces the statistical ensemble, which is a large collection of virtual, independent copies of the system in various states. The statistical ensemble is a probability distribution over all possible states of the system. In classical statistical mechanics, the ensemble is a probability distribution over phase points (as opposed to a single phase point in ordinary mechanics), usually represented as a distribution in a phase space with canonical coordinates. In quantum statistical mechanics, the ensemble is a probability distribution over pure states, and can be compactly summarized as a density matrix.

普通力学只考虑单一状态的行为，而统计力学引入了统计系综，它是系统在各种状态下的大量虚拟、独立副本的集合。系综是一个覆盖系统所有可能状态的概率分布。在经典的统计力学中，系综是相点上的概率分布(与普通力学中的单相点相反) ，通常表现为正则坐标下相空间中的分布。在量子统计力学中，系综是纯态上的概率分布，可以简单地概括为密度矩阵。

普通力学只考虑单一状态的行为，而统计力学引入了<font color="#FF8000">统计系综 statistical ensemble</font>，它是系统在各种状态下的大量虚拟、独立副本的集合。系综是一个覆盖系统所有可能状态的<font color="#FF8000">概率分布 probability distribution</font>。在经典的统计力学中，系综是相点上的概率分布(与普通力学中的单相点相反) ，通常表现为<font color="#FF8000">正则坐标 canonical coordinates</font>下相空间中的分布。在量子统计力学中，系综是纯态上的概率分布，可以简单地概括为<font color="#FF8000">密度矩阵 density matrix</font>。