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第503行：
第503行： − 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。+ − 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。+ 第532行：
第532行： − +
→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
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名义值相结合，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。
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名义值。
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.
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随时间变化趋势"。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涨落期间进行的，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标称值。除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。
"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随时间变化趋势"。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名义值相对应，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涨落期间进行的，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。除非已知属于平衡状态的名义值，否则根据单一的度量无法进行判断。
=== Thermal equilibrium ===
=== Thermal equilibrium ===