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In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.
In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.
为了使一个系统处于它自己的内部热力学平衡状态，它处于自己内部的热平衡状态当然是必要的，但不是充分的;系统在达到内部热平衡之前，可以达到内部机械平衡。如上所述，根据 A.Münster的说法，对于给定的孤立系统的任何状态，定义一个热力学平衡所需的变量数是最少的。如上所述，J.G.Kirkwood 和 I.Oppenheim 指出，热力学平衡状态可以由一个特殊的子类的强变量定义，该子类中有一定数量的成员。
Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.
Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable [[temperature]]. According to [[Edward A. Guggenheim|E.A. Guggenheim]], "The most important conception of thermodynamics is temperature."<ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967), p.5.</ref> Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."<ref name="Planck 1903 3">[[Max Planck|Planck, M.]] (1897/1927), p.3.</ref> As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.