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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi,  M.G. (1955/2005), p. 4.</ref> 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 his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.<ref name="Caratheodory" /> In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."<ref>Prigogine, I., Defay, R. (1950/1954), p. 1.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi,  M.G. (1955/2005), p. 4.</ref> 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.

在他关于封闭系统平衡态热力学方案的论述中，C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题，当我们确定了一个系统的一定数量的宏观属性，那么所有其他属性都是固定的。如上所述，A. Münster认为，对于给定孤立系统的任何状态来说，定义热力学平衡所需的变量数量是最少的。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集约变量来定义，该子类中有一定数量的成员。

在他关于封闭系统平衡态热力学方案的论述中，C.Carathéodory 最初假定实验揭示了一定数量的实变量定义了作为平衡态流形点的状态。用 Prigogine 和 Defay (1945)的话说: “这是一个经验问题，当我们确定了一个系统一定数量的宏观属性时，那么所有其他属性都是固定的。如上所述，A. Münster认为，定义热力学平衡所需的变量数量对于给定孤立系统的任何状态来说都是最少的。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子类的强度变量来定义，该子类中有一定数量的成员。

When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.

When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.

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，它自发地发展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，在这种演变的许多情况下，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，在这种演变的许多情况下，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，在这种演变的许多情况下，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，在这种演变的许多情况下，热平衡的发展要比化学平衡快得多。

If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.

If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.

如果热力学平衡位于一个外力场中，那么通常只有温度在空间上是均匀的。如果外力场非零，温度以外的强度变量通常是不均匀的。在这种情况下，一般需要附加变量来描述空间非均匀性。

如果热力学平衡位于一个外力场中，那么通常只有温度在空间上是均匀的。如果外力场非零，温度以外的强度变量通常是不均匀的。在这种情况下，一般需要附加变量来描述空间非均匀性。

===Stability against small perturbations===

===Stability against small perturbations===