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→Derivation from statistical mechanics
The first mechanical argument of the Kinetic theory of gases that molecular collisions entail an equalization of temperatures and hence a tendency towards equilibrium was due to James Clerk Maxwell in 1860; Ludwig Boltzmann with his H-theorem of 1872 also argued that due to collisions gases should over time tend toward the Maxwell–Boltzmann distribution.
The first mechanical argument of the Kinetic theory of gases that molecular collisions entail an equalization of temperatures and hence a tendency towards equilibrium was due to James Clerk Maxwell in 1860; Ludwig Boltzmann with his H-theorem of 1872 also argued that due to collisions gases should over time tend toward the Maxwell–Boltzmann distribution.
'''气体动力学Kinetic theory of gases'''理论的第一个力学论证由'''詹姆斯·克拉克·麦克斯韦James Clerk Maxwell'''在1860年给出，指出分子碰撞引起温度均衡，因此整体趋向于平衡； '''路德维希·玻尔兹曼Ludwig Boltzmann'''在1872年提出的''' H 定理H-theorem'''也认为，气体由于碰撞应该随着时间的推移趋向于'''麦克斯韦-波兹曼分布Maxwell–Boltzmann distribution'''。
'''<font color="#ff8000">气体动力学Kinetic theory of gases</font>'''理论的第一个力学论证由'''<font color="#ff8000">麦克斯韦James Clerk Maxwell</font>'''在1860年给出，指出分子碰撞引起温度均衡<font color = 'blue'>化</font>，因此整体趋向于'''<font color="#ff8000">平衡 Equilibrium </font>'''； '''<font color="#ff8000">玻尔兹曼Ludwig Boltzmann</font>'''在1872年提出的'''<font color="#ff8000"> H 定理H-theorem</font>'''也认为，气体由于碰撞应该随着时间的推移趋向于'''<font color="#ff8000">麦克斯韦-波兹曼分布Maxwell–Boltzmann distribution</font>'''。
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Loschmidt's paradox'''，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Correlation and dependence|uncorrelated'''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boundary condition'''，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Big Bang''') 。也有人提出了其他假设。
由于'''<font color="#ff8000">洛施密特悖论Loschmidt's paradox</font>'''，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'''<font color="#ff8000">边界条件boundary condition</font>'''，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('''<font color="#ff8000">大爆炸 the Big Bang</font>''') ，<font color = 'blue'>尽管</font>也有人提出了其他<font color = 'red'><s>假设</s></font><font color = 'blue'>场景</font>。
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:
<font color = 'red'><s>考虑到</s></font><font color = 'blue'>基于</font>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Statistical mechanics#Fundamental postulate|fundamental postulate'''的一个结果，也被称为'''<font color="#ff8000">等先验概率假设 equal prior probability postulate</font>'''。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。<font color = 'red'><s>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。</s></font>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<font color = 'blue'>即热孤立系统的熵只能增加，</font>是等先验概率假设的一个显然结果。处于热平衡状态的孤立系统<font color = 'red'><s>包含</s></font><font color = 'blue'>且具有</font>能量<math>E</math>的熵表示为：
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