Thermodynamics

"Madoka, do you know the word "entropy"?" ~ Kyubey's fail-lecture regarding entropy in Episode 9

File:QB loves entropy.jpg

Kyubey loves Entropy too!

The Laws of Thermodynamics hold significant importance to the story as the basis of Kyubey's motivation.

Entropy

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/cm3, or 0,889767627 joules/km^3. The expansion rate of the universe, again as determined by WMAP observations is roughly 71.9 (km/s)/Mpc, 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 862800 kilometers of radius per second, which comes down to a volume gain of 1.48656647 × 10^54 kilometers cubed per second.

Thus, in order to maintain the energy density of the universe (admittedly, though, there are better ways to preserve life) 1.32269872 × 10^54 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 3.31249766 × 10^52 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 6,2802117 × 10^17 times the current age of the universe.

B. Create 3,68565071 × 10^35 kilograms of any matter (except cheese.) This comes down to about 184027 sun-sized stars, 61 billion Earth-sized planets or a single supermassive black hole with a radius of 547298,036 kilometers, roughly 1,4 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.

• 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.