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→Fluctuations within an isolated system in its own internal thermodynamic equilibrium
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.
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。