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==Derivation from statistical mechanics==

==Derivation from statistical mechanics==

{{Further information|H-theorem}}

{{Further information|H-theorem}}

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.

分子运动论的第一个机械论证是分子碰撞引起温度均衡，因此趋向于平衡，这是由于1860年的詹姆斯·克拉克·麦克斯韦; 路德维希·玻尔兹曼和他的1872年的 h 定理也认为，由于碰撞气体应该随着时间的推移趋向于麦克斯韦-波兹曼分布。

气体动力学理论的第一个力学论证由詹姆斯·克拉克·麦克斯韦在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·玻尔兹曼在1872年提出的 H 定理也认为，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。

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.

由于洛斯密特的悖论，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间是不相关的; 这允许简单的概率处理。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) ，尽管也有人提出了其他假设。

数学 dS  frac {1}{ t } sum { j } e { j } dP { j } frac {1}{ t }{ j }{ j }向左(e { j } p { j }右)-frac {1}{ t }{ j }和{ j }向右(t }{ j }向右)-frac {1}{ j }向右(t }{ j }向左)-frac { j }向右(t }{ j }向右(t }向右)-f rc { j }{ j }向右(t }向右(t)向右(t }向右)-f rc { j }向右(t }向右) -

数学 dS  frac {1}{ t } sum { j } e { j } dP { j } frac {1}{ t }{ j }{ j }向左(e { j } p { j }右)-frac {1}{ t }{ j }和{ j }向右(t }{ j }向右)-frac {1}{ j }向右(t }{ j }向左)-frac { j }向右(t }{ j }向右(t }向右)-f rc { j }{ j }向右(t }向右(t)向右(t }向右)-f rc { j }向右(t }向右) -

==Living organisms==

==Living organisms==