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Take for example (experiment A) a closed box that is, at the beginning, half-filled with ideal gas. As time passes, the gas obviously expands to fill the whole box, so that the final state is a box full of gas. This is an irreversible process, since if the box is full at the beginning (experiment B), it does not become only half-full later, except for the very unlikely situation where the gas particles have very special locations and speeds. But this is precisely because we always assume that the initial conditions are such that the particles have random locations and speeds. This is not correct for the final conditions of the system, because the particles have interacted between themselves, so that their locations and speeds have become dependent on each other, i.e. correlated. This can be understood if we look at experiment A backwards in time, which we'll call experiment C: now we begin with a box full of gas, but the particles do not have random locations and speeds; rather, their locations and speeds are so particular, that after some time they all move to one half of the box, which is the final state of the system (this is the initial state of experiment A, because now we're looking at the same experiment backwards!). The interactions between particles now do not create correlations between the particles, but in fact turn them into (at least seemingly) random, "canceling" the pre-existing correlations. The only difference between experiment C (which defies the Second Law of Thermodynamics) and experiment B (which obeys the Second Law of Thermodynamics) is that in the former the particles are uncorrelated at the end, while in the latter the particles are uncorrelated at the beginning.

Take for example (experiment A) a closed box that is, at the beginning, half-filled with ideal gas. As time passes, the gas obviously expands to fill the whole box, so that the final state is a box full of gas. This is an irreversible process, since if the box is full at the beginning (experiment B), it does not become only half-full later, except for the very unlikely situation where the gas particles have very special locations and speeds. But this is precisely because we always assume that the initial conditions are such that the particles have random locations and speeds. This is not correct for the final conditions of the system, because the particles have interacted between themselves, so that their locations and speeds have become dependent on each other, i.e. correlated. This can be understood if we look at experiment A backwards in time, which we'll call experiment C: now we begin with a box full of gas, but the particles do not have random locations and speeds; rather, their locations and speeds are so particular, that after some time they all move to one half of the box, which is the final state of the system (this is the initial state of experiment A, because now we're looking at the same experiment backwards!). The interactions between particles now do not create correlations between the particles, but in fact turn them into (at least seemingly) random, "canceling" the pre-existing correlations. The only difference between experiment C (which defies the Second Law of Thermodynamics) and experiment B (which obeys the Second Law of Thermodynamics) is that in the former the particles are uncorrelated at the end, while in the latter the particles are uncorrelated at the beginning.

举个例子(实验A)，一个封闭的盒子，一开始是半满的理想气体。随着时间的推移，气体明显膨胀到装满整个盒子，所以最终的状态是一个装满气体的盒子。这是一个不可逆转的过程，因为如果盒子在一开始是满的(实验B)，它不会在之后变得只有半满，除了非常不可能的情况，即气体颗粒具有非常特殊的位置和速度。但这恰恰是因为我们总是假设初始条件中粒子具有随机的位置和速度。这对于系统的最终条件是不正确的，因为粒子之间已经进行了相互作用，以至于它们的位置和速度已经变得相互依赖，即相互关联。如果我们倒着看实验A（称之为实验C），这是可以理解的：现在我们从一个装满气体的盒子开始，但粒子没有随机的位置和速度；相反，它们的位置和速度很特殊，以至于一段时间后，它们都移动到盒子的半边，达到系统的最终状态(这是实验A的初始状态，因为现在我们正在反向管看相同的实验！)。粒子之间的相互作用现在不会使粒子之间产生关联，而实际上是将它们变成(至少看起来是)随机的，“取消”先前存在的关联。实验C(违反热力学第二定律)和实验B(遵守热力学第二定律)之间的唯一区别是，在前者中，粒子在结束时是不相关的，而在后者中，粒子在开始时是不相关的。

举个例子(实验A)，一个封闭的盒子，一开始是半满的理想气体。随着时间的推移，气体明显膨胀到装满整个盒子，所以最终的状态是一个装满气体的盒子。这是一个不可逆转的过程，因为如果盒子在一开始是满的(实验B)，它不会在之后变得只有半满，除了非常不可能的情况，即气体颗粒具有非常特殊的位置和速度。但这恰恰是因为我们总是假设初始条件中粒子具有随机的位置和速度。这对于系统的最终条件是不正确的，因为粒子之间已经进行了相互作用，以至于它们的位置和速度已经变得相互依赖，即相互关联。如果我们倒着看实验A（称之为实验C），这是可以理解的：现在我们从一个装满气体的盒子开始，但粒子没有随机的位置和速度；相反，它们的位置和速度很特殊，以至于一段时间后，它们都移动到盒子的半边，达到系统的最终状态(这是实验A的初始状态，因为现在我们正在反向管看相同的实验！)。粒子之间的相互作用现在不会使粒子之间产生关联，而实际上是将它们变成(至少看起来是)随机的，“取消”先前存在的关联。实验C(违反热力学第二定律)和实验B(遵守热力学第二定律)之间的唯一区别是，在前者中，粒子在结束时不相关，而在后者中，粒子在开始时不相关。

In fact, if all the microscopic physical processes are reversible (see discussion below), then the Second Law of Thermodynamics can be proven for any isolated system of particles with initial conditions in which the particles states are uncorrelated. To do this, one must acknowledge the difference between the measured entropy of a system—which depends only on its [[macrostate]] (its volume, temperature etc.)—and its [[information entropy]],<ref>''Physical Origins of Time Asymmetry'', p. 35.</ref> which is the amount of information (number of computer bits) needed to describe the exact [[microstate (statistical mechanics)|microstate]] of the system. The measured entropy is independent of correlations between particles in the system, because they do not affect its macrostate, but the information entropy '''does''' depend on them, because correlations lower the randomness of the system and thus lowers the amount of information needed to describe it.<ref>''Physical Origins of Time Asymmetry'', pp. 35-38.</ref> Therefore, in the absence of such correlations the two entropies are identical, but otherwise the information entropy is smaller than the measured entropy, and the difference can be used as a measure of the amount of correlations.

In fact, if all the microscopic physical processes are reversible (see discussion below), then the Second Law of Thermodynamics can be proven for any isolated system of particles with initial conditions in which the particles states are uncorrelated. To do this, one must acknowledge the difference between the measured entropy of a system—which depends only on its [[macrostate]] (its volume, temperature etc.)—and its [[information entropy]],<ref>''Physical Origins of Time Asymmetry'', p. 35.</ref> which is the amount of information (number of computer bits) needed to describe the exact [[microstate (statistical mechanics)|microstate]] of the system. The measured entropy is independent of correlations between particles in the system, because they do not affect its macrostate, but the information entropy '''does''' depend on them, because correlations lower the randomness of the system and thus lowers the amount of information needed to describe it.<ref>''Physical Origins of Time Asymmetry'', pp. 35-38.</ref> Therefore, in the absence of such correlations the two entropies are identical, but otherwise the information entropy is smaller than the measured entropy, and the difference can be used as a measure of the amount of correlations.