| Due to Loschmidt's paradox, derivations of the Second Law have to make an assumption regarding the past, namely that the system is uncorrelated at some time in the past; this allows for simple probabilistic treatment. This assumption is usually thought as a boundary condition, and thus the second Law is ultimately a consequence of the initial conditions somewhere in the past, probably at the beginning of the universe (the Big Bang), though other scenarios have also been suggested. | | Due to Loschmidt's paradox, derivations of the Second Law have to make an assumption regarding the past, namely that the system is uncorrelated at some time in the past; this allows for simple probabilistic treatment. This assumption is usually thought as a boundary condition, and thus the second Law is ultimately a consequence of the initial conditions somewhere in the past, probably at the beginning of the universe (the Big Bang), though other scenarios have also been suggested. |
− | 由于洛施密特悖论,第二定律的导出必须对过去做出一个假设,即系统在过去的某个时刻是不相关的;这样的假设允许进行简单的概率处理。这个假设通常被认为是一个边界条件,因此热力学第二定律最终是过去某个地方的初始条件的结果,可能是在宇宙的开始(大爆炸) ,尽管也有人提出了其他假设。 | + | 由于洛施密特悖论,第二定律的导出必须对过去做出一个假设,即系统在过去的某个时刻是不相关的;这样的假设允许进行简单的概率处理。这个假设通常被认为是一个边界条件,因此热力学第二定律最终是过去某个地方的初始条件的结果,可能是在宇宙的开始(大爆炸) 。也有人提出了其他假设。 |
| Given these assumptions, in statistical mechanics, the Second Law is not a postulate, rather it is a consequence of the fundamental postulate, also known as the equal prior probability postulate, so long as one is clear that simple probability arguments are applied only to the future, while for the past there are auxiliary sources of information which tell us that it was low entropy. The first part of the second law, which states that the entropy of a thermally isolated system can only increase, is a trivial consequence of the equal prior probability postulate, if we restrict the notion of the entropy to systems in thermal equilibrium. The entropy of an isolated system in thermal equilibrium containing an amount of energy of <math>E</math> is: | | Given these assumptions, in statistical mechanics, the Second Law is not a postulate, rather it is a consequence of the fundamental postulate, also known as the equal prior probability postulate, so long as one is clear that simple probability arguments are applied only to the future, while for the past there are auxiliary sources of information which tell us that it was low entropy. The first part of the second law, which states that the entropy of a thermally isolated system can only increase, is a trivial consequence of the equal prior probability postulate, if we restrict the notion of the entropy to systems in thermal equilibrium. The entropy of an isolated system in thermal equilibrium containing an amount of energy of <math>E</math> is: |
− | 考虑到这些假设,在21统计力学,第二定律不是一个假设,而是基本假设的一个结果,也被称为等先验概率假设,只要一个人清楚地知道,简单的概率论证只适用于未来,而对于过去,有辅助的信息来源告诉我们,它是低熵的。第二定律的第一部分指出,热孤立系统的熵只能增加,如果我们把熵的概念限制在热平衡系统中,那么第二定律的第一部分是等价的先验概率假设的一个微不足道的结果。在热平衡,一个孤立系统的熵包含数学 e / math 的能量是:
| + | 考虑到这些假设,在统计力学中,第二定律不是一个假设,而是统计力学基本假设的一个结果,也被称为等先验概率假设。这个基本假设表明,只要一个人清楚地知道,简单的概率论证只适用于未来,而对于过去,有辅助的信息来源告诉我们,它是低熵的。热力学第二定律的第一部分指出,热孤立系统的熵只能增加。如果我们把熵的概念限制在热平衡系统中,那么热力学第二定律的第一部分是等先验概率假设的一个显然结果。在热平衡,一个孤立系统的熵包含数学 e / math 的能量是: |