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第491行： − + − − − If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent. − − 如果系统被重复细分，最终产生的系统足够小，可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此，精确地选择独立状态变量是很重要的。在这个阶段，热力学定律的统计特征变得明显。 − − In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account. − − 在一个孤立的系统中，根据定义，热力学平衡可以持续无限长的时间。在经典物理学中，忽略测量的影响通常是很方便的，现在我们假设这一点。 − − If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important. − − 如果介观系统进一步重复分裂，最终产生一个微观系统。物质的分子性质和动量传递的量子性质在波动过程中起着重要作用。这已经离开了经典热力学或宏观热力学的领域，即需要量子统计力学。波动可以变得相对占主导地位，测量问题变得重要。 − 考虑孤立热力学系统中的波动概念，一个方便的例子是由其众多的状态变量，内能、体积和质量组成指定的系统。根据定义，它们是时不变的。根据定义，它们与它们的共轭状态密集函数的时不变名义值相结合，反向温度，压力除以温度，化学势除以温度，以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值，不足以提供这些名义值的知识。我们需要进一步的信息，即关于该系统的构成特性的信息。 − 考虑孤立热力学系统中的波动概念，一个方便的例子是由其广泛的状态变量、内能、体积和质量组成指定的系统。根据定义，它们是时不变的。根据定义，它们与它们的共轭状态密集函数的时不变名义值相结合，反向温度，压力除以温度，化学势除以温度，以便准确地服从热力学定律。但是热力学定律加上指定广泛的状态变量的值，不足以提供这些名义值的知识。我们需要进一步的信息，即关于该系统的构成特性的信息。+ − − − The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state. − "系统是它自己的内部热力学平衡"的说法可能意味着"无限期地，许多这样的测量是不时进行的，在各种测量值中没有时间趋势"。因此，一个系统处于它自己的内部热力学平衡，它的状态变量与它状态变量共轭函数的标称值相对应，这种说法远比“一个状态函数的一组单一的同时测量值具有相同的值”的说法丰富得多。这是因为单个测量可能是在轻微波动期间进行的，而不是由于未知和不同的构成属性而导致的，即远离那些共轭的状态密集函数的另一组名义值。非已知属于平衡状态的标称值，否则根据单一的度量无法进行判断。 − 可以承认，在重复测量这些共轭强度函数时，发现它们的值随时间略有不同。这种可变性被认为是由于内部波动。不同测量值平均到其名义值。+ 第534行：
第516行： − 如果这个系统真的像经典热力学所假定的那样是宏观的，那么这个系统的波动太小了，宏观上无法检测到。这就是所谓的热力学极限。实际上，物质的分子性质和动量转移的量子性质由于它们太小而看不见，已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中，平衡的波动概念是没有位置的。”+ − 如果系统被重复细分，最终产生的系统足够小，可以表现出明显的波动。这是一个介观层面的研究。波动则直接取决于系统各壁的性质。因此，精确地选择独立状态变量是很重要的。在这个阶段，热力学定律的统计特征变得明显。+
→Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始，然后被孤立，它会自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如，在这种演化的许多情况下，内部力学平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是，在这种演化的许多情况下，热平衡的发展要比化学平衡快得多。
当一个物质体从不均匀的非平衡状态或化学非平衡状态开始，然后被孤立，它会自发地演化到自己的内部热力学平衡状态。没有必要同时达到内部热力学平衡的所有方面; 有些方面可以先于其他方面建立起来。例如，在这种演化的许多情况下，内部力学平衡的建立比最终热力学平衡的其他方面要快得多。另一个例子是，在这种演化的许多情况下，热平衡的发展要比化学平衡快得多。
===Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的===
===Fluctuations within an isolated system in its own internal thermodynamic equilibrium 孤立系统内部热力学平衡的涨落===
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.
在一个孤立的系统中，根据定义，热力学平衡可以持续无限长的时间。在经典物理学中，忽略测量的影响通常是很方便的，现在我们假设这一点。
在一个孤立的系统中，根据定义，热力学平衡可以持续无限长的时间。在经典物理学中，忽略测量的影响通常是很方便的，现在我们假设这一点。
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.<ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 21.</ref> But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.
考虑孤立热力学系统中的涨落概念，一个方便的例子是由其内能、体积和质量组成等广延量表示的系统。根据定义，它们是不随时间变化的。根据定义，这些量与它们的共轭状态强度函数的时不变标称值相结合，包括逆温度，压力除以温度，化学势除以温度，以便准确地服从热力学定律。但是热力学定律加上指定广延量的值，不足以提供这些标称值的知识。我们需要进一步的信息，即关于该系统的构成特性的信息。
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.
可以承认，在重复测量这些共轭强度状态函数时，发现它们的值随时间略有不同。这种可变性被认为是由于内部涨落。不同测量值平均到其标称值。
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."
如果系统真的像经典热力学所假定的那样是宏观的，那么系统的涨落很小以至于宏观上无法检测到。这就是所谓的热力学极限。实际上，物质的分子性质和动量转移的量子性质由于它们太小而看不见，已经从我们的视线中消失。根据Buchdahl: “ ... 在严格的现象学理论中，平衡的涨落概念是不存在的。”
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.
如果系统被重复细分，最终产生的系统足够小，可以表现出明显的涨落。这是一个介观层面的研究。涨落则直接取决于系统各壁的性质。因此，精确地选择独立状态变量是很重要的。在这个阶段，热力学定律的统计特征变得明显。
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.