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第4行： − − 熵是物理科学中唯一需要特定时间方向的量(除了粒子物理学中某些罕见的相互作用，见下文) ，有时被称为时间之箭。热力学第二定律认为，随着时间的推移，孤立系统的熵可以增加，但不会减少。因此，从一个角度来看，熵测量是一种区分过去和未来的方法。然而，在不封闭的热力学系统中，熵会随着时间而减少: 许多系统，包括生命系统，以牺牲环境的增加为代价减少局部熵，导致熵的净增加。这类系统和现象的例子包括热力学中所用的典型晶体的形成、冰箱的工作原理和活的有机体。 第13行：
第11行： − 就像温度一样，尽管是一个抽象的概念，每个人对熵的影响都有一种直观的感觉。例如，通常很容易区分正在播放的视频和正在播放的前后。一段视频可能描述了一场融化附近冰块的木柴大火，反过来播放的话，就会显示出一滩水把一团烟雾变成了未燃烧的木头，并在此过程中把自己冻结了。令人惊讶的是，在这两种情况下，绝大多数物理定律都没有被这些过程打破，一个明显的例外是热力学第二定律。当一个物理定律同样适用于时间被反转的情况时，它被称为 t 对称性，在这种情况下，熵允许人们判断上面描述的视频是正向播放还是反向播放，因为我们直观地认为，只有当正向播放时，场景的熵才会增加。由于热力学第二定律的存在，熵阻止了宏观过程呈现 t 对称性。+ 第36行：
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第375行： − − + − − |last=Mackey − − |first=Michael C. − − |title=Time's Arrow: The Origins of Thermodynamic Behavior − − |year=1992 − − |publisher=Springer − − |location=Berlin Heidelberg New York − − |isbn=3-540-94093-6 − − |oclc=28585247 − − |quote=... it is shown that for there to be a global evolution of the entropy to its maximal value ... it is ''necessary and sufficient'' that the system have a property known as exactness. ... these criteria suggest that all currently formulated physical laws may not be at the foundation of the thermodynamic behavior we observe every day of our lives. (page xi) 第459行：
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翻译第二段
Entropy is the only quantity in the physical sciences (apart from certain rare interactions in particle physics; see below) that requires a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system can increase, but not decrease. Hence, from one perspective, entropy measurement is a way of distinguishing the past from the future. However, in thermodynamic systems that are not closed, entropy can decrease with time: many systems, including living systems, reduce local entropy at the expense of an environmental increase, resulting in a net increase in entropy. Examples of such systems and phenomena include the formation of typical crystals, the workings of a refrigerator and living organisms, used in thermodynamics.
Entropy is the only quantity in the physical sciences (apart from certain rare interactions in particle physics; see below) that requires a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system can increase, but not decrease. Hence, from one perspective, entropy measurement is a way of distinguishing the past from the future. However, in thermodynamic systems that are not closed, entropy can decrease with time: many systems, including living systems, reduce local entropy at the expense of an environmental increase, resulting in a net increase in entropy. Examples of such systems and phenomena include the formation of typical crystals, the workings of a refrigerator and living organisms, used in thermodynamics.
熵是物理科学中 (除了粒子物理学中某些罕见的相互作用；见下文) 唯一需要特定的时间方向的量，时间的方向有时被称为时间之箭。热力学第二定律显示，随着时间的推移，孤立系统的熵可能增加，但不会减少。因此，从某个角度来看，熵的测量是区分过去和未来的一种方式。然而，在非封闭的热力学系统中，熵可能随时间减少：许多系统，包括生命系统，以环境熵的增加为代价减少局部熵，导致熵的净增加。在热力学中，这些系统和现象的例子包括典型晶体的形成、冰箱的工作原理以及生物体。
熵是物理科学中 (除了粒子物理学中某些罕见的相互作用；见下文) 唯一需要特定的时间方向的量，时间的方向有时被称为时间之箭。热力学第二定律显示，随着时间的推移，孤立系统的熵可能增加，但不会减少。因此，从某个角度来看，熵的测量是区分过去和未来的一种方式。然而，在非封闭的热力学系统中，熵可能随时间减少：许多系统，包括生命系统，以环境熵的增加为代价减少局部熵，导致熵的净增加。在热力学中，这些系统和现象的例子包括典型晶体的形成、冰箱的工作原理以及生物体。
Much like temperature, despite being an abstract concept, everyone has an intuitive sense of the effects of entropy. For example, it is often very easy to tell the difference between a video being played forwards or backwards. A video may depict a wood fire that melts a nearby ice block, played in reverse it would show that a puddle of water turned a cloud of smoke into unburnt wood and froze itself in the process. Surprisingly, in either case the vast majority of the laws of physics are not broken by these processes, a notable exception being the second law of thermodynamics. When a law of physics applies equally when time is reversed, it is said to show T-symmetry, in this case entropy is what allows one to decide if the video described above is playing forwards or in reverse as intuitively we identify that only when played forwards the entropy of the scene is increasing. Because of the second law of thermodynamics, entropy prevents macroscopic processes showing T-symmetry.
Much like temperature, despite being an abstract concept, everyone has an intuitive sense of the effects of entropy. For example, it is often very easy to tell the difference between a video being played forwards or backwards. A video may depict a wood fire that melts a nearby ice block, played in reverse it would show that a puddle of water turned a cloud of smoke into unburnt wood and froze itself in the process. Surprisingly, in either case the vast majority of the laws of physics are not broken by these processes, a notable exception being the second law of thermodynamics. When a law of physics applies equally when time is reversed, it is said to show T-symmetry, in this case entropy is what allows one to decide if the video described above is playing forwards or in reverse as intuitively we identify that only when played forwards the entropy of the scene is increasing. Because of the second law of thermodynamics, entropy prevents macroscopic processes showing T-symmetry.
虽然熵像温度一样是抽象概念，但每个人对熵的影响都有直观感觉。例如，人们区分一条视频是正放还是倒放通常很容易。倒放一段关于木头燃烧融化附近冰块的视频，原过程就会变为一滩水把一团烟雾变成了未燃烧的木头，并在这个过程中冻结了自己。令人惊讶的是，在任何情况下，绝大多数物理定律都没有被这些过程打破，但热力学第二定律是一个值得注意的例外。如果物理定律在时间倒转时同样适用，那么它就表现出了T对称，在这种情况下，熵使人们有能力分辨上述视频是正放还是倒放的，因为我们可以直观地发现，只有在正放时，场景的熵才会增加。基于热力学第二定律，熵阻止宏观过程呈现T对称。
== Overview==
==Overview==
The [[Second Law of Thermodynamics]] allows for the entropy to ''remain the same'' regardless of the direction of time. If the entropy is constant in either direction of time, there would be no preferred direction. However, the entropy can only be a constant if the system is in the highest possible state of disorder, such as a gas that always was, and always will be, uniformly spread out in its container. The existence of a thermodynamic arrow of time implies that the system is highly ordered in one time direction only, which would by definition be the "past". Thus this law is about the [[boundary conditions]] rather than the [[equations of motion]].
The [[Second Law of Thermodynamics]] allows for the entropy to ''remain the same'' regardless of the direction of time. If the entropy is constant in either direction of time, there would be no preferred direction. However, the entropy can only be a constant if the system is in the highest possible state of disorder, such as a gas that always was, and always will be, uniformly spread out in its container. The existence of a thermodynamic arrow of time implies that the system is highly ordered in one time direction only, which would by definition be the "past". Thus this law is about the [[boundary conditions]] rather than the [[equations of motion]].
热力学箭头通常与宇宙学的时间箭头联系在一起，因为它最终与早期宇宙的边界条件有关。根据大爆炸理论，宇宙最初是非常热的，能量分布均匀。对于一个引力很重要的系统，比如宇宙，这是一个低熵状态(与所有物质坍缩成黑洞的高熵状态相比，系统最终可能进化到这种状态)。随着宇宙的发展，它的温度下降，这使得未来可用于工作的能量比过去要少。此外，能量密度中的扰动也在增加(最终形成星系和恒星)。因此，宇宙本身有一个定义明确的热力学时间箭头。但是这并没有解决为什么宇宙的初始状态是低熵的问题。如果宇宙膨胀由于引力而停止或逆转，那么宇宙的温度将再次升高，但是由于扰动的持续增长和最终黑洞的形成，宇宙的熵也将继续增加，直到大坍缩的后期，那时的熵将比现在低。
热力学箭头通常与宇宙学的时间箭头联系在一起，因为它最终与早期宇宙的边界条件有关。根据大爆炸理论，宇宙最初是非常热的，能量分布均匀。对于一个引力很重要的系统，比如宇宙，这是一个低熵状态(与所有物质坍缩成黑洞的高熵状态相比，系统最终可能进化到这种状态)。随着宇宙的发展，它的温度下降，这使得未来可用于工作的能量比过去要少。此外，能量密度中的扰动也在增加(最终形成星系和恒星)。因此，宇宙本身有一个定义明确的热力学时间箭头。但是这并没有解决为什么宇宙的初始状态是低熵的问题。如果宇宙膨胀由于引力而停止或逆转，那么宇宙的温度将再次升高，但是由于扰动的持续增长和最终黑洞的形成，宇宙的熵也将继续增加，直到大坍缩的后期，那时的熵将比现在低。
现在想象一下这个实验重复进行，这次只有几个分子，也许十个，在一个非常小的容器里。人们可以很容易地想象，通过观察分子的随机碰撞，它可能发生---- 仅仅是偶然---- 分子整齐地分离开来，所有的染料分子在一边，所有的水分子在另一边。这种情况可以不时地发生，这可以从涨落定理中得出结论; 因此分子彼此分离并不是不可能的。然而，对于大量的分子来说，它是如此的不可能，以至于人们不得不等待，平均而言，要比宇宙的年龄长很多倍的时间才能发生。因此，如果一部电影像上面描述的那样展示了大量的分子自我分离，这看起来是不现实的，人们会倾向于说这部电影是以相反的方式播放的。把玻尔兹曼第二定律看作是无序定律。
现在想象一下这个实验重复进行，这次只有几个分子，也许十个，在一个非常小的容器里。人们可以很容易地想象，通过观察分子的随机碰撞，它可能发生---- 仅仅是偶然---- 分子整齐地分离开来，所有的染料分子在一边，所有的水分子在另一边。这种情况可以不时地发生，这可以从涨落定理中得出结论; 因此分子彼此分离并不是不可能的。然而，对于大量的分子来说，它是如此的不可能，以至于人们不得不等待，平均而言，要比宇宙的年龄长很多倍的时间才能发生。因此，如果一部电影像上面描述的那样展示了大量的分子自我分离，这看起来是不现实的，人们会倾向于说这部电影是以相反的方式播放的。把玻尔兹曼第二定律看作是无序定律。
时间箭头、熵和热力学第二定律的基础背后的数学来源于以下的设置，详见卡诺(1824)、克拉佩龙(1832)和克劳修斯(1854) :
时间箭头、熵和热力学第二定律的基础背后的数学来源于以下的设置，详见卡诺(1824)、克拉佩龙(1832)和克劳修斯(1854) :
接下来，如果我们像最初由克劳修斯所做的那样做作业:
接下来，如果我们像最初由克劳修斯所做的那样做作业:
那么这个变换的熵变或“等价值”是:
那么这个变换的熵变或“等价值”是:
这等于:
这等于:
通过分解 q，我们得到了下面的形式，正如克劳修斯所推导的:
通过分解 q，我们得到了下面的形式，正如克劳修斯所推导的:
因此，举例来说，如果 q 是50个单位，t1 / sub 最初是100度，t2 / sub 最初是1度，那么这个过程的熵变为49.5。因此，这个过程的熵增加了，这个过程需要一定的“时间” ，并且熵增加与时间的流逝相关。因此，对于这种系统配置，它是一个“绝对规则”。这一规则是基于这样一个事实，即所有的自然过程都是不可逆的，因为一个系统的分子，例如一个罐中的两个分子，不仅做外部功(如推动活塞) ，而且根据过程中所用的热量(见: 热量的机械等效物)相互作内部功。熵解释了分子间存在内部摩擦的事实。
因此，举例来说，如果 q 是50个单位，t1 / sub 最初是100度，t2 / sub 最初是1度，那么这个过程的熵变为49.5。因此，这个过程的熵增加了，这个过程需要一定的“时间” ，并且熵增加与时间的流逝相关。因此，对于这种系统配置，它是一个“绝对规则”。这一规则是基于这样一个事实，即所有的自然过程都是不可逆的，因为一个系统的分子，例如一个罐中的两个分子，不仅做外部功(如推动活塞) ，而且根据过程中所用的热量(见: 热量的机械等效物)相互作内部功。熵解释了分子间存在内部摩擦的事实。
现在，根据刘维尔定理，所有微观过程的时间反转意味着描述孤立系统精确微观状态所需要的信息量(其信息论联合熵)在时间上是不变的。这个联合熵等于边际熵(假设没有相关性)加上相关熵(互熵，或其负互信息)。如果我们最初假设粒子之间没有相关性，那么这个联合熵就是边际熵，也就是系统的初始熵，除以玻耳兹曼常数。然而，如果这些确实是初始条件(这是一个关键的假设) ，那么这种相关性与时间形成。换句话说，存在一个减少的互熵(或增加的互信息) ，并且在不太长的时间内，粒子之间的关联(互信息)只随时间增加。因此，与边际熵成正比的熵也必须随着时间而增加(注意，在这种情况下，“不要太久”是相对于经典系统版本所需的时间，以便它通过所有可能的微观状态ーー这个时间可以粗略地估计为数学 τ e ^ s / math，其中 math tau / math 是粒子碰撞和 s 之间的时间，s 是系统的熵。在任何实际的情况下，这个时间是巨大的比其他任何事情)。注意，粒子之间的相关性并不是一个完全客观的量。我们不能测量互熵，我们只能测量它的变化，假设我们可以测量一个微观状态。热力学仅限于微观状态无法区分的情况，这意味着只有与熵成正比的边际熵才能被测量，而且，在实际意义上，总是在增加。
现在，根据刘维尔定理，所有微观过程的时间反转意味着描述孤立系统精确微观状态所需要的信息量(其信息论联合熵)在时间上是不变的。这个联合熵等于边际熵(假设没有相关性)加上相关熵(互熵，或其负互信息)。如果我们最初假设粒子之间没有相关性，那么这个联合熵就是边际熵，也就是系统的初始熵，除以玻耳兹曼常数。然而，如果这些确实是初始条件(这是一个关键的假设) ，那么这种相关性与时间形成。换句话说，存在一个减少的互熵(或增加的互信息) ，并且在不太长的时间内，粒子之间的关联(互信息)只随时间增加。因此，与边际熵成正比的熵也必须随着时间而增加(注意，在这种情况下，“不要太久”是相对于经典系统版本所需的时间，以便它通过所有可能的微观状态ーー这个时间可以粗略地估计为数学 τ e ^ s / math，其中 math tau / math 是粒子碰撞和 s 之间的时间，s 是系统的熵。在任何实际的情况下，这个时间是巨大的比其他任何事情)。注意，粒子之间的相关性并不是一个完全客观的量。我们不能测量互熵，我们只能测量它的变化，假设我们可以测量一个微观状态。热力学仅限于微观状态无法区分的情况，这意味着只有与熵成正比的边际熵才能被测量，而且，在实际意义上，总是在增加。
所有在一个时间方向上行为不同的现象最终都可以与热力学第二定律联系起来。这包括冰块在热咖啡中融化而不是从咖啡中自己组合出来，在粗糙的表面上滑动的冰块减慢而不是加速，以及我们能记住过去而不是未来。事实上，如果人们把记忆看作是脑细胞(或计算机比特)和外部世界之间的联系，那么就很容易理解它与热力学第二定律的联系。
所有在一个时间方向上行为不同的现象最终都可以与热力学第二定律联系起来。这包括冰块在热咖啡中融化而不是从咖啡中自己组合出来，在粗糙的表面上滑动的冰块减慢而不是加速，以及我们能记住过去而不是未来。事实上，如果人们把记忆看作是脑细胞(或计算机比特)和外部世界之间的联系，那么就很容易理解它与热力学第二定律的联系。
目前的研究主要集中在用数学方法描述经典系统和量子系统中的时间热力学箭头，以及从宇宙学边界条件的角度理解其来源。
目前的研究主要集中在用数学方法描述经典系统和量子系统中的时间热力学箭头，以及从宇宙学边界条件的角度理解其来源。
截至2006年，这种类型的时间对称性破缺已被证明只有很少数量的精确可解的，离散时间系统。较复杂系统的转移算子没有得到一致的规定，其精确定义也陷入了各种微妙的困难之中。特别是，对于最简单的精确可解连续时间遍历系统，如 Hadamard 台球系统，或 PSL (2，r)切空间上的 Anosov 流动，还没有证明它具有破对称性。
截至2006年，这种类型的时间对称性破缺已被证明只有很少数量的精确可解的，离散时间系统。较复杂系统的转移算子没有得到一致的规定，其精确定义也陷入了各种微妙的困难之中。特别是，对于最简单的精确可解连续时间遍历系统，如 Hadamard 台球系统，或 PSL (2，r)切空间上的 Anosov 流动，还没有证明它具有破对称性。
另一种截然不同的方法是通过量子混沌的研究，试图将系统量子化为经典的混沌、遍历或混合。得到的结果与转移算子法的结果没有什么不同。例如，玻耳兹曼气体的量子化，即矩形盒中的硬(弹性)点粒子气体，揭示了本征函数是占据整个盒子的填充空间的分形，能量本征值的间隔非常紧密，并且有一个“几乎连续”的谱(对于一个盒子中有限数目的粒子，谱必然是离散的)。如果初始条件是这样的，所有的粒子都局限在箱子的一边，系统很快演化为一个粒子填充整个箱子。实际上，即使所有的粒子最初都在盒子的一边，它们的波函数也会渗透到整个盒子里: 它们在一边建设性地干涉，在另一边破坏性地干涉。不可逆性的论点是，波函数”几乎不可能”被”偶然地”安排在某种不可能的状态: 这种安排是一组零测度。因为本征函数是分形的，所以熵和统计力学的大部分语言和机制可以用来讨论和论证量子情况。
另一种截然不同的方法是通过量子混沌的研究，试图将系统量子化为经典的混沌、遍历或混合。得到的结果与转移算子法的结果没有什么不同。例如，玻耳兹曼气体的量子化，即矩形盒中的硬(弹性)点粒子气体，揭示了本征函数是占据整个盒子的填充空间的分形，能量本征值的间隔非常紧密，并且有一个“几乎连续”的谱(对于一个盒子中有限数目的粒子，谱必然是离散的)。如果初始条件是这样的，所有的粒子都局限在箱子的一边，系统很快演化为一个粒子填充整个箱子。实际上，即使所有的粒子最初都在盒子的一边，它们的波函数也会渗透到整个盒子里: 它们在一边建设性地干涉，在另一边破坏性地干涉。不可逆性的论点是，波函数”几乎不可能”被”偶然地”安排在某种不可能的状态: 这种安排是一组零测度。因为本征函数是分形的，所以熵和统计力学的大部分语言和机制可以用来讨论和论证量子情况。
目前还不清楚在这种情况下，热力学第二定律会发生什么。我们可以想象至少有三种不同的情况(事实上，只有第三种情况是可信的，因为前两种情况需要宇宙平稳演化，这与我们观察到的情况相反) :
目前还不清楚在这种情况下，热力学第二定律会发生什么。我们可以想象至少有三种不同的情况(事实上，只有第三种情况是可信的，因为前两种情况需要宇宙平稳演化，这与我们观察到的情况相反) :
* A highly controversial view is that in such a case the arrow of time will reverse.<ref>{{Cite journal |doi = 10.1103/PhysRevD.32.2489|pmid = 9956019|bibcode = 1985PhRvD..32.2489H|title = Arrow of time in cosmology|year = 1985|last1 = Hawking|first1 = S. W.|journal = Physical Review D|volume = 32|issue = 10|pages = 2489–2495}}</ref> The quantum fluctuations—which in the meantime have evolved into galaxies and stars—will be in [[Superposition principle|superposition]] in such a way that the whole process described above is reversed—i.e., the fluctuations are erased by [[destructive interference]] and total uniformity is achieved once again. Thus the universe ends in a [[Big Crunch]], which is similar to its beginning in the [[Big Bang]]. Because the two are totally symmetric, and the final state is very highly ordered, entropy must decrease close to the end of the universe, so that the Second Law of Thermodynamics reverses when the universe shrinks. This can be understood as follows: in the very early universe, interactions between fluctuations created [[Quantum entanglement|entanglement]] ([[quantum correlation]]s) between particles spread all over the universe; during the expansion, these particles became so distant that these correlations became negligible (see [[quantum decoherence]]). At the time the expansion halts and the universe starts to shrink, such correlated particles arrive once again at contact (after circling around the universe), and the entropy starts to decrease—because highly correlated initial conditions may lead to a decrease in entropy. Another way of putting it, is that as distant particles arrive, more and more order is revealed because these particles are highly correlated with particles that arrived earlier.
* A highly controversial view is that in such a case the arrow of time will reverse.<ref>{{Cite journal |doi = 10.1103/PhysRevD.32.2489|pmid = 9956019|bibcode = 1985PhRvD..32.2489H|title = Arrow of time in cosmology|year = 1985|last1 = Hawking|first1 = S. W.|journal = Physical Review D|volume = 32|issue = 10|pages = 2489–2495}}</ref> The quantum fluctuations—which in the meantime have evolved into galaxies and stars—will be in [[Superposition principle|superposition]] in such a way that the whole process described above is reversed—i.e., the fluctuations are erased by [[destructive interference]] and total uniformity is achieved once again. Thus the universe ends in a [[Big Crunch]], which is similar to its beginning in the [[Big Bang]]. Because the two are totally symmetric, and the final state is very highly ordered, entropy must decrease close to the end of the universe, so that the Second Law of Thermodynamics reverses when the universe shrinks. This can be understood as follows: in the very early universe, interactions between fluctuations created [[Quantum entanglement|entanglement]] ([[quantum correlation]]s) between particles spread all over the universe; during the expansion, these particles became so distant that these correlations became negligible (see [[quantum decoherence]]). At the time the expansion halts and the universe starts to shrink, such correlated particles arrive once again at contact (after circling around the universe), and the entropy starts to decrease—because highly correlated initial conditions may lead to a decrease in entropy. Another way of putting it, is that as distant particles arrive, more and more order is revealed because these particles are highly correlated with particles that arrived earlier.
* It could be that this is the crucial point where the [[wavefunction collapse]] is important: if the collapse is real, then the quantum fluctuations will not be in superposition any longer; rather they had collapsed to a particular state (a particular arrangement of galaxies and stars), thus creating a [[Big Crunch]], which is very different from the [[Big Bang]]. Such a scenario may be viewed as adding [[boundary conditions]] (say, at the distant future) that dictate the wavefunction collapse.<ref>{{Cite arxiv |eprint=quant-ph/0507269 |title = Two-time interpretation of quantum mechanics g|last1 = Gruss|first1 = Eyal Y.|last2 = Aharonov|first2 = Yakir|year = 2005}}</ref>
*It could be that this is the crucial point where the [[wavefunction collapse]] is important: if the collapse is real, then the quantum fluctuations will not be in superposition any longer; rather they had collapsed to a particular state (a particular arrangement of galaxies and stars), thus creating a [[Big Crunch]], which is very different from the [[Big Bang]]. Such a scenario may be viewed as adding [[boundary conditions]] (say, at the distant future) that dictate the wavefunction collapse.<ref>{{Cite arxiv |eprint=quant-ph/0507269 |title = Two-time interpretation of quantum mechanics g|last1 = Gruss|first1 = Eyal Y.|last2 = Aharonov|first2 = Yakir|year = 2005}}</ref>
* The broad consensus among the scientific community today is that smooth initial conditions lead to a highly non-smooth final state, and that this is in fact the source of the thermodynamic arrow of time.<ref>{{Cite journal |doi = 10.4249/scholarpedia.3448|bibcode = 2008SchpJ...3.3448L|title = Time's arrow and Boltzmann's entropy|year = 2008|last1 = Lebowitz|first1 = Joel|journal = Scholarpedia|volume = 3|issue = 4|pages = 3448|doi-access = free}}</ref> Highly non-smooth [[gravity|gravitational]] systems tend to collapse to [[black hole]]s, so the [[wavefunction]] of the whole universe evolves from a [[Superposition principle|superposition]] of small fluctuations to a [[Superposition principle|superposition]] of states with many [[black hole]]s in each. It may even be that it is impossible for the universe to have both a smooth beginning and a smooth ending. Note that in this scenario the energy density of the universe in the final stages of its shrinkage is much larger than in the corresponding initial stages of its expansion (there is no [[destructive interference]], unlike in the first scenario described above), and consists of mostly black holes rather than free particles.
*The broad consensus among the scientific community today is that smooth initial conditions lead to a highly non-smooth final state, and that this is in fact the source of the thermodynamic arrow of time.<ref>{{Cite journal |doi = 10.4249/scholarpedia.3448|bibcode = 2008SchpJ...3.3448L|title = Time's arrow and Boltzmann's entropy|year = 2008|last1 = Lebowitz|first1 = Joel|journal = Scholarpedia|volume = 3|issue = 4|pages = 3448|doi-access = free}}</ref> Highly non-smooth [[gravity|gravitational]] systems tend to collapse to [[black hole]]s, so the [[wavefunction]] of the whole universe evolves from a [[Superposition principle|superposition]] of small fluctuations to a [[Superposition principle|superposition]] of states with many [[black hole]]s in each. It may even be that it is impossible for the universe to have both a smooth beginning and a smooth ending. Note that in this scenario the energy density of the universe in the final stages of its shrinkage is much larger than in the corresponding initial stages of its expansion (there is no [[destructive interference]], unlike in the first scenario described above), and consists of mostly black holes rather than free particles.
在第二种和第三种情况下，宇宙的初始状态和最终状态之间的差异决定了时间的热力学箭头。这与宇宙时间之箭无关。在第二种情况下，时间的量子箭头可能被视为这种现象的深层原因。
在第二种和第三种情况下，宇宙的初始状态和最终状态之间的差异决定了时间的热力学箭头。这与宇宙时间之箭无关。在第二种情况下，时间的量子箭头可能被视为这种现象的深层原因。
==See also==
==See also==
* [[Arrow of time]]
*[[Arrow of time]]
* [[Cosmic inflation]]
*[[Cosmic inflation]]
* [[Entropy]]
*[[Entropy]]
* [[History of entropy]]
* [[History of entropy]]
* [[H-theorem]]
*[[H-theorem]]
*[[Loschmidt's paradox]]
{{reflist}}
{{reflist}}
==Further reading==
==Further reading==
* {{cite book | first = J.J. | last = Halliwell | title = Physical Origins of Time Asymmetry| publisher = Cambridge | year = 1994| isbn = 0-521-56837-4|display-authors=etal}} (technical).
*{{cite book | first = J.J. | last = Halliwell | title = Physical Origins of Time Asymmetry| publisher = Cambridge | year = 1994| isbn = 0-521-56837-4|display-authors=etal}} (technical).
* {{cite book
* {{cite book
|last=Mackey
|last=Mackey
最后一个麦基
最后一个麦基
|first=Michael C.
|first=Michael C.
首先是迈克尔 · c。
首先是迈克尔 · c。
|title=Time's Arrow: The Origins of Thermodynamic Behavior
|title=Time's Arrow: The Origins of Thermodynamic Behavior
时间之箭: 热力学行为的起源
时间之箭: 热力学行为的起源
|year=1992
|year=1992
1992年
1992年
|publisher=Springer
|publisher=Springer
出版商斯普林格
出版商斯普林格
|location=Berlin Heidelberg New York
|location=Berlin Heidelberg New York
| 地点: Berlin Heidelberg New York
| 地点: Berlin Heidelberg New York
|isbn=3-540-94093-6
|isbn=3-540-94093-6
| isbn 3-540-94093-6
| isbn 3-540-94093-6
|oclc=28585247
|oclc=28585247
28585247
28585247
|quote=... it is shown that for there to be a global evolution of the entropy to its maximal value ... it is necessary and sufficient that the system have a property known as exactness. ... these criteria suggest that all currently formulated physical laws may not be at the foundation of the thermodynamic behavior we observe every day of our lives. (page xi)
|quote=... it is shown that for there to be a global evolution of the entropy to its maximal value ... it is necessary and sufficient that the system have a property known as exactness. ... these criteria suggest that all currently formulated physical laws may not be at the foundation of the thermodynamic behavior we observe every day of our lives. (page xi)
}}<br/> Dover has reprinted the monograph in 2003 ({{ISBN|0486432432}}). For a short paper listing "the essential points of that argument, correcting presentation points that were confusing ... and emphasizing conclusions more forcefully than previously" see {{cite book |last=Mackey | first=Michael C. | editor1-first=C. | editor1-last=Mugnai |editor2-first=A. | editor2-last=Ranfagni |editor3-first=L.S. | editor3-last=Schulman |title=Time's Arrow, Quantum Measurement and Superluminal Behavior |publisher=Consiglio Nazionale Delle Ricerche| location=Rome |year=2001 |pages=49–65 |chapter=Microscopic Dynamics and the Second Law of Thermodynamics |chapterurl=http://www.cnd.mcgill.ca/bios/mackey/pdf_pub/newfinalnaples.pdf |isbn=88-8080-024-8| archive-url=https://web.archive.org/web/20110725021113/http://www.cnd.mcgill.ca/bios/mackey/pdf_pub/newfinalnaples.pdf | archive-date=2011-07-25 }}
}}<br/> Dover has reprinted the monograph in 2003 ({{ISBN|0486432432}}). For a short paper listing "the essential points of that argument, correcting presentation points that were confusing ... and emphasizing conclusions more forcefully than previously" see {{cite book |last=Mackey | first=Michael C. | editor1-first=C. | editor1-last=Mugnai |editor2-first=A. | editor2-last=Ranfagni |editor3-first=L.S. | editor3-last=Schulman |title=Time's Arrow, Quantum Measurement and Superluminal Behavior |publisher=Consiglio Nazionale Delle Ricerche| location=Rome |year=2001 |pages=49–65 |chapter=Microscopic Dynamics and the Second Law of Thermodynamics |chapterurl=http://www.cnd.mcgill.ca/bios/mackey/pdf_pub/newfinalnaples.pdf |isbn=88-8080-024-8| archive-url=https://web.archive.org/web/20110725021113/http://www.cnd.mcgill.ca/bios/mackey/pdf_pub/newfinalnaples.pdf | archive-date=2011-07-25 }}
}}<br/> Dover has reprinted the monograph in 2003 (). For a short paper listing "the essential points of that argument, correcting presentation points that were confusing ... and emphasizing conclusions more forcefully than previously" see
<nowiki>}}</nowiki><br /> Dover has reprinted the monograph in 2003 (). For a short paper listing "the essential points of that argument, correcting presentation points that were confusing ... and emphasizing conclusions more forcefully than previously" see
} br / Dover 在2003年重印了该专著。一篇简短的论文列出“论点的要点，纠正混乱的陈述观点... ... 并比以前更有力地强调结论”见
} br / Dover 在2003年重印了该专著。一篇简短的论文列出“论点的要点，纠正混乱的陈述观点... ... 并比以前更有力地强调结论”见
* [[Sean M. Carroll]], ''[[From Eternity to Here: The Quest for the Ultimate Theory of Time]]''
*[[Sean M. Carroll]], ''[[From Eternity to Here: The Quest for the Ultimate Theory of Time]]''
==External links==
==External links==
* [http://plato.stanford.edu/entries/time-thermo/ Thermodynamic Asymmetry in Time] at the online [[Stanford Encyclopedia of Philosophy]]
*[http://plato.stanford.edu/entries/time-thermo/ Thermodynamic Asymmetry in Time] at the online [[Stanford Encyclopedia of Philosophy]]