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第718行：
第718行： − 另一类重要的非平衡统计力学模型处理的系统，只有非常轻微的扰动从平衡。在很小的扰动下，响应可以用线性响应理论进行分析。一个显著的结果，正如涨落耗散定理的形式化，是系统的反应时，接近平衡恰恰相关的涨落，发生时，系统是在总平衡。从本质上讲，一个系统如果稍微偏离平衡，无论是由于外力还是由于波动，都会以同样的方式向平衡方向放松，因为这个系统既不能说出差别，也不能“知道”它是如何偏离平衡的。+ 第726行：
第726行： − 这提供了一个间接的方法，通过从平衡电导率和热导率统计力学中提取结果来获得诸如欧姆电导率和电导率之类的数字。由于平衡统计力学在数学上有很好的定义，而且(在某些情况下)更易于计算，因此在近平衡统计力学中，涨落-耗散连接可以成为一种方便的计算捷径。+ 第734行：
第734行： − 用于建立这种联系的一些理论工具包括:+ 第746行：
第746行： + + + + + + + +
→Near-equilibrium methods
Another important class of non-equilibrium statistical mechanical models deals with systems that are only very slightly perturbed from equilibrium. With very small perturbations, the response can be analysed in linear response theory. A remarkable result, as formalized by the fluctuation-dissipation theorem, is that the response of a system when near equilibrium is precisely related to the fluctuations that occur when the system is in total equilibrium. Essentially, a system that is slightly away from equilibrium—whether put there by external forces or by fluctuations—relaxes towards equilibrium in the same way, since the system cannot tell the difference or "know" how it came to be away from equilibrium.
Another important class of non-equilibrium statistical mechanical models deals with systems that are only very slightly perturbed from equilibrium. With very small perturbations, the response can be analysed in linear response theory. A remarkable result, as formalized by the fluctuation-dissipation theorem, is that the response of a system when near equilibrium is precisely related to the fluctuations that occur when the system is in total equilibrium. Essentially, a system that is slightly away from equilibrium—whether put there by external forces or by fluctuations—relaxes towards equilibrium in the same way, since the system cannot tell the difference or "know" how it came to be away from equilibrium.
非平衡态统计力学模型处理的另一类重要的系统，是对平衡态仅有非常轻微扰动的系统。在很小的扰动下，响应可以用线性响应理论进行分析。涨落-耗散定理是其中一个重要的结果，近平衡态系统的响应与系统总体平衡时的涨落准确相关。从本质上讲，一个系统如果稍微偏离平衡，无论是由于外力还是由于涨落，都会以同样的方式向平衡方向弛豫。因为这个系统无法区分偏离和回归，也“不知道”它是如何偏离平衡的。
This provides an indirect avenue for obtaining numbers such as ohmic conductivity and thermal conductivity by extracting results from equilibrium statistical mechanics. Since equilibrium statistical mechanics is mathematically well defined and (in some cases) more amenable for calculations, the fluctuation-dissipation connection can be a convenient shortcut for calculations in near-equilibrium statistical mechanics.
This provides an indirect avenue for obtaining numbers such as ohmic conductivity and thermal conductivity by extracting results from equilibrium statistical mechanics. Since equilibrium statistical mechanics is mathematically well defined and (in some cases) more amenable for calculations, the fluctuation-dissipation connection can be a convenient shortcut for calculations in near-equilibrium statistical mechanics.
这提供了一个间接的方法，通过从平衡态统计力学中提取结果来获得诸如欧姆电导率和热导率之类的物理量。由于平衡态统计力学在数学上有很好的定义，而且(在某些情况下)更易于计算，因此在近平衡态统计力学中，涨落-耗散关联可以成为一种方便的计算捷径。
A few of the theoretical tools used to make this connection include:
A few of the theoretical tools used to make this connection include:
用于建立这种关联的一些理论工具包括:
* [[Fluctuation–dissipation theorem]]
* [[Fluctuation–dissipation theorem]]
* [[Mori–Zwanzig formalism]]
* [[Mori–Zwanzig formalism]]
* [[涨落-耗散定理]]
* [[昂萨格倒易关系]]
* [[格林-库伯关系]]
* [[Ballistic conduction#Landauer-Büttiker formalism|Landauer–Büttiker 公式]]
* [[Mori–Zwanzig 公式]]
=== Hybrid methods ===
=== Hybrid methods ===