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Suppose we have an isolated system whose macroscopic state is specified by a number of variables. These macroscopic variables can, e.g., refer to the total volume, the positions of pistons in the system, etc. Then <math>\Omega</math> will depend on the values of these variables. If a variable is not fixed, (e.g. we do not clamp a piston in a certain position), then because all the accessible states are equally likely in equilibrium, the free variable in equilibrium will be such that <math>\Omega</math> is maximized as that is the most probable situation in equilibrium.

Suppose we have an isolated system whose macroscopic state is specified by a number of variables. These macroscopic variables can, e.g., refer to the total volume, the positions of pistons in the system, etc. Then <math>\Omega</math> will depend on the values of these variables. If a variable is not fixed, (e.g. we do not clamp a piston in a certain position), then because all the accessible states are equally likely in equilibrium, the free variable in equilibrium will be such that <math>\Omega</math> is maximized as that is the most probable situation in equilibrium.

假设我们有一个孤立系统，其宏观状态由许多变量描述。这些宏观变量可以是总体积、活塞在系统中的位置等。从而<math>\Omega</math>将取决于这些变量的值。如果某个变量不是固定的（我们不会在某个位置夹住活塞) ，那么因为在平衡状态下所有可到达状态的等几率到达的，平衡状态下的自由变量会使 <math>\Omega</math> 最大，因为这是平衡状态下最可能的情况。

假设我们有一个孤立系统，其宏观状态由许多变量<font color = 'red'><s>描述</s></font><font color = 'blue'>指定</font>。这些宏观变量可以是总体积、活塞在系统中的位置等。从而<math>\Omega</math>将取决于这些变量的值。如果某个变量不是固定的（我们不会在某个位置夹住活塞) ，那么因为在平衡状态下<font color = 'red'><s>所有可到达状态的等几率到达的，</s></font><font color = 'blue'>到达所有可到达状态的可能性是相等的，</font>平衡状态下的自由变量会使 <math>\Omega</math> 最大，因为这是平衡状态下最可能的情况。

 

If the variable was initially fixed to some value then upon release and when the new equilibrium has been reached, the fact the variable will adjust itself so that <math>\Omega</math> is maximized, implies that the entropy will have increased or it will have stayed the same (if the value at which the variable was fixed happened to be the equilibrium value).

If the variable was initially fixed to some value then upon release and when the new equilibrium has been reached, the fact the variable will adjust itself so that <math>\Omega</math> is maximized, implies that the entropy will have increased or it will have stayed the same (if the value at which the variable was fixed happened to be the equilibrium value).