玻尔兹曼大脑是玻尔兹曼关于热力学时间箭头解释的理论预测。虽然路德维希·波尔兹曼本人从未讨论过这个概念，但当宇宙学家运用他关于随机涨落的观点来理解整个宇宙时，这个概念就产生了。

波尔兹曼脑背景

路德维希·波尔兹曼是十九世纪热力学领域的奠基人之一。其中一个关键概念是热力学第二定律，即封闭系统的熵总是增加的。由于宇宙是一个封闭的系统，我们预计熵会随着时间的推移而增加。这意味着，给定足够的时间，宇宙最有可能的状态是万物处于热力学平衡状态，但我们显然不存在于这种类型的宇宙中，因为毕竟，我们周围有各种形式的秩序，其中最重要的是我们存在的事实。

考虑到这一点，我们可以应用人择原理，考虑到我们确实存在，从而为我们的推理提供信息。这里的逻辑有点混乱，所以我们将借用两个更详细的例子。正如宇宙学家肖恩·卡罗尔在《从永恒到这里：

Boltzmann invoked the anthropic principle (although he didn't call it that) to explain why we wouldn't find ourselves in one of the very common equilibrium phases: In equilibrium, life cannot exist. Clearly, what we want to do is find the most common conditions within such a universe that are hospitable to life. Or, if we want to be more careful, perhaps we should look for conditions that are not only hospitable to life, but hospitable to the particular kind of intelligent and self-aware life that we like to think we are....

We can take this logic to its ultimate conclusion. If what we want is a single planet, we certainly don't need a hundred billion galaxies with a hundred billion stars each. And if what we want is a single person, we certainly don't need an entire planet. But if in fact what we want is a single intelligence, able to think about the world, we don't even need an entire person--we just need his or her brain.

So the reductio ad absurdum of this scenario is that the overwhelming majority of intelligences in this multiverse will be lonely, disembodied brains, who fluctuate gradually out of the surrounding chaos and then gradually dissolve back into it. Such sad creatures have been dubbed "Boltzmann brains" by Andreas Albrecht and Lorenzo Sorbo....

在2004年的一篇论文中，Albrecht和Sorbo在论文中讨论了“玻尔兹曼大脑”：

A century ago Boltzmann considered a “cosmology” where the observed universe should be regarded as a rare fluctuation out of some equilibrium state. The prediction of this point of view, quite generically, is that we live in a universe which maximizes the total entropy of the system consistent with existing observations. Other universes simply occur as much more rare fluctuations. This means as much as possible of the system should be found in equilibrium as often as possible.

From this point of view, it is very surprising that we find the universe around us in such a low entropy state. In fact, the logical conclusion of this line of reasoning is utterly solipsistic. The most likely fluctuation consistent with everything you know is simply your brain (complete with “memories” of the Hubble Deep fields, WMAP data, etc) fluctuating briefly out of chaos and then immediately equilibrating back into chaos again. This is sometimes called the “Boltzmann’s Brain” paradox.

这些描述的要点并不是暗示玻尔兹曼大脑确实存在。有点像薛定谔的猫思维实验，这种思维实验的目的是将事物延伸到最极端的结论，以此来显示这种思维方式的潜在局限性和缺陷。玻尔兹曼大脑的理论存在让你可以用它们作为一个修辞的例子，从热力学涨落中表现出一些荒谬的东西，就像卡罗尔说的那样“热辐射的随机波动将导致各种不太可能的事件——包括星系、行星和玻尔兹曼大脑的自发产生。”

既然你已经把玻尔兹曼大脑理解为一个概念，那么你必须继续理解“玻尔兹曼大脑悖论”，这是由于将这种思维运用到如此荒谬的程度而引起的。同样，正如卡罗尔所说：

Why do we find ourselves in a universe evolving gradually from a state of incredibly low entropy, rather than being isolated creatures that recently fluctuated from the surrounding chaos?

不幸的是，没有明确的解释来解决这个问题。。。因此，为什么它仍然被归类为悖论。卡罗尔的书着重于试图解决它提出的关于宇宙熵和宇宙时间之箭的问题。

大众文化与玻尔兹曼的大脑

有趣的是，玻尔兹曼的大脑以两种不同的方式进入了大众文化。他们在一部迪尔伯特漫画中以一个快速的笑话出现，在一部《不可思议的大力士》中以外星人入侵者的身份出现