This BBC special "Wonders of the Universe" is an excellent refresher course on Entropy.
In Episode 9, Kyubey explains that delaying maximum Entropy, or heat death of the universe, is his reason for contracting magical girls. When QB's scientifically-advanced civilization discovered Magic, they realized Magic's capacity to create new energy can postpone maximum Entropy and delay the heat death of the Universe. However, QB's civilization are incapable of emotions, thus they scoured the Universe for species with the most emotional potential. QB found his answer in the Earth's human females, especially those still developing secondary sex characteristics.
 Time travel
Homura's wish gives her the unique ability to travel back in time. The irreversible increase of entropy is the empirical justification for arrow of time that separates the past and the future. Homura's time traveling reverses the arrow of time, thus in effect reduced entropy. This may explains Kyubey's unique monologue for Homura's soul gem ceremony,
"the contract is concluded. Your wish has surpassed entropy." ~ Kyubey in Episode 10
 Energy generation
Assume Incubators are trying to sustain the entire universe using the misery of little girls. According to data gathered by the Wilkinson Microwave Anisotrophy Probe (WMAP), energy density of the universe comes down to roughly 9.9 x 10-30 g.cm-3, or 0.89 joules.km-3. The expansion rate of the universe, again as determined by WMAP observations is roughly 71.9 km.s-1.Mpc-1, ignoring other studies. The minimum radius of the universe, as determined by cosmic microwave background radiation data, is 12 gigaparsecs. Consequently, the universe gains at least 860000 kilometers of radius per second, which comes down to a volume gain of 1.5 × 1054 km3.s-1.
Thus, in order to maintain the energy density of the universe (admittedly, though, there are better ways to preserve life) 1.32 × 1054 joules is required every second. Let us use high estimates and say that there is one magical girl for every 1,000 people. As of now, there are roughly 6.9 billion living people, so there are 6,900,000 magical girls across the world. Assume that every magical girl defeats a witch every two days, and hands over her Grief Seed to an Incubator for its energy to be collected. This comes down to roughly 40 witches being defeated every second. Therefore, if the energy density of the universe is to be maintained, every Grief Seed needs to have an energy output of at least 3.3 × 1052 joules. What can you do with this sort of energy?
- A. Supply the Earth’s energy needs for roughly 8.6 octillion years, a timespan 6 × 1024 times the current age of the universe.
- B. Create 3.7 × 1043 kilograms of any matter. This comes down to about 184,027 sun-sized stars, 61 billion Earth-sized planets or a single supermassive black hole with a radius of 547,298,036 kilometers, roughly 14 times the distance between Earth and the Moon.
- C. In a single year, enough energy is collected to create roughly 10 galaxies the size of our Milky Way.
- D. Create a single explosion a few hundred thousand times stronger than any gamma ray burst we've observed so far. This would end most, if not all life (at least carbon-based life as we know it) pretty much everywhere from Earth to Andromeda galaxy.
Personally, the only reason I can muster for this bizarre turn is that the writers want to change the setting. In the previous episodes, QB has become a bit too obviously antagonistic, making him a villain of sorts. But this development changes things, making QB not a villain but an act of god. Something outside human power. So the objective here becomes not “winning,” but rather “surviving.”
However, it should also be noted that this series of calculations assumes that Earth is the only source of emotional beings located by the Incubators. This is never explicitly stated to be the case; all that is stated is that their own species lacks them. Thus, if there are other worlds with emotional beings, the burden on Earth's population would be greatly lessened. And given the size of the universe and the Incubators' civilisation's evident technological advancement (allowing them, one presumes, to travel it fairly easily), this does seem fairly likely, especially considering how Kyubey is not interested to the Earth fate in Episode 10.
- Kyubey never mentions maintaining the energy density of the universe. His species' goal is simply to battle entropy by subverting the law of conservation of energy, thus the estimates for the amount of energy contained in a grief seed don't need to be nearly that high.
- On the other hand, Kyubey could be just lying and trying to use the issue of entropy as a form of deception as a way to lure Puellae Magi to sacrifice their lives for a noble cause. However, given the ending of the series, it leaves open the idea that the universe is ending because of entropy as a plausible explanation.
 Further reading
- Last question by Isaac Asimov - A short story set near heat death of the universe.
- understanding entropy - a page regarding entropy.
 Youtube Videos
- The Problem with Entropy - The problem with the 2nd Law of Thermodynamics (Entropy in the universe is always increasing) is that it does not apply to life's increasing complexity, societal evolution, technological progression, nor consciousness.
- The Arrow of Time feat. Sean Carroll - Why is the past different from the future? Caltech physicist Sean Carroll explains how the arrow of time is not an intrinsic property of physics, but rather an emergent feature.
- Entropy: Embrace the Chaos! Crash Course Chemistry #20 - Life is chaos and the universe tends toward disorder. But why? If you think about it, there are only a few ways for things to be arranged in an organized manner, but there are nearly infinite other ways for those same things to be arranged. Simple rules of probability dictate that it's much more likely for stuff to be in one of the many disorganized states than in one of the few organized states. This tendency is so unavoidable that it's known as the 2nd Law of Thermodynamics. Obviously, disorder is a pretty big deal in the universe and that makes it a pretty big deal in chemistry - it's such a big deal that scientists have a special name for it: entropy. In chemistry, entropy is the measure of molecular randomness, or disorder. For the next thirteen minutes, Hank hopes you will embrace the chaos as he teaches you about entropy.
- Parallel Universes, Alternative Timelines & Multiverse - BBC Horizon - Scientists now believe there may really be a parallel universe - in fact, there may be an infinite number of parallel universes, and we just happen to live in one of them. These other universes contain space, time and strange forms of exotic matter. Some of them may even contain you, in a slightly different form. Astonishingly, scientists believe that these parallel universes exist less than one millimetre away from us. In fact, our gravity is just a weak signal leaking out of another universe into ours.
- The Fabric of the Cosmos: Universe or Multiverse? - Recent developments in cosmology and particle physics, such as the string landscape picture, have led to the remarkable realization that our universe - rather than being unique - could be just one of many universes. The multiverse proposal helps to explain the origin of the universe and some of its observational features. Since the physical constants can be different in other universes, the fine-tunings which appear necessary for the emergence of life may also be explained. Nevertheless, many physicists remain uncomfortable with the multiverse proposal, since it is highly speculative and perhaps untestable.
- Michio Kaku Explains String Theory - Theoretical physicist Michio Kaku explains the basics of String Theory in this clip from his Floating University lecture.
- Multiverse Parallel Universes - Some of the world's leading physicists believe they have found startling new evidence showing the existence of universes other than our own. One possibility is that the universe is so vast that an exact replica of our Solar System, our planet and ourselves exists many times over. These Doppelganger Universes exist within our own Universe; in what scientist now call "The Multiverse." Today, trailblazing experiments by state of the art particle colliders are looking for evidence of higher dimensions and Parallel Universes. If proof is found, it will change our lives, our minds, our planet, our science and our universe.
- The Fabric Of The Cosmos - The Illusion Of Time? - This program challenges our traditional questions about time such as; does it flow in one direction or does it flow at all? Does everyone experience the same now? Is time travel possible? Will time come to an end?
- The Hawking Paradox - Stephen Hawking, plays the role of great troublemaker by breaking the Universe, then ultimately fixing it again before anyone else could prove that it was never really broken. This show discusses how black holes could break the law of the conservation of information. Ultimately the problem is fixed via a form of radiation now called Hawking radiation, which "projects" a "holographic image" of the matter and the information about the matter that is sucked in. In short, black holes exist and at the same time they do not exist, if we believe that there are other parallel universes where black holes dont exist parallel to ours where they do exist...
- The True Science of Parallel Universes - Explaining the science behind parallel universes in minutes.
- White Holes: An Impossible Possibility - In general relativity, a white hole is a hypothetical region of spacetime which cannot be entered from the outside, although matter and light can escape from it. In this sense, it is the reverse of a black hole, which can only be entered from the outside, but from which nothing, including light, can escape. Theoretically, a White Hole could reverse entropy.
- ↑ The point of this video is that 'there is a problem with applying the 2nd Law of Thermodynamics with the living world.' Erwin Schrödinger introduced the term "negentropy" to address this problem. In a world governed by the second law of thermodynamics, all closed systems are expected to approach a state of maximum disorder. In contrast, life approaches and maintains a highly ordered state - which seems to violate aforementioned second law. The solution to this paradox is that life is not a closed system. The increase of order inside an organism is more than paid for by an increase in disorder outside this organism. By this mechanism, the second law is obeyed, and life maintains a high order state (negentropy), which it sustains by causing a net increase in disorder in the Universe (entropy).