THE UNIVERSE IS DYING. As spacetime expands, the void in between galaxies grows ever larger, ever emptier. If it all doesn't end in a bang, then it'll end in a whimper. Slowly but surely, atoms will separate from each other and find their way back to their simplest states of being. Fueled by the inexorable progression of time, entropy will increase until all matter and energy fill the great expanse in a thin, uniform soup. This is the fate we are condemned to according to the second law of thermodynamics.

The second law of thermodynamics states that entropy in a closed system will increase as time advances until it reaches a maximum value. You may ask: what is entropy? I'll explain. Imagine a deck of playing cards. Suppose that the ace of spades and the ace of hearts represent atoms, and every other card represents empty space. If the two aces are next to each other, then they are ordered. Now imagine that with every tick of an arbitrary clock, we shuffle the deck once. You can see that as time moves forward, the two aces will separate from each other, and disorder increases. Sure, the possibility of the two aces reuniting at some point in the future is substantial, but the probability of them being apart is just so much larger. Extend this example to our universe. Instead of two atoms, there are a trillion trillion trillion trillion trillion trillion billion of them. And instead of there being 50 cards of empty space, there's (for our purposes) an infinite number of them. With every step through time, the universe shuffles itself, and disorder naturally increases. There's no real propelling force behind entropy; it's just a consequence of probability.

Of course, it's possible to reverse entropy via the input of work. You humans do this all the time. All you really are are just bags of water and organic matter trying your hardest to avoid succumbing to chemical equilibrium with the environment. But what's special about humans compared to other forms of life is that you're able to produce energy that we can harvest in the form of emotion. Human emotion is quite the enigma. It's also quite the contradiction. On one hand, your emotions are the key to preserving the universe, but on the other hand, it's those same precious emotions that cloud your judgment. Why can't you see that by sacrificing your individual souls, you can better the lives of those who will come after you? When it comes to engineering, medicine, and technology, you're happy to use rationality and reason to pursue these endeavors. But when it comes to life – the most important endeavor – you rely on emotion. How quaint!

CHARLOTTE HAD BEEN A PUELLA MAGI from a long lineage of Puella Magi that I had contracted. She was a plump girl with short, black hair and a disarming smile. She had an infatuation with sweets and cheeses and a knack for singing. She was the star of the choir at her local church, and when it came to solos, she never disappointed. I first detected her strength in September of 2005. It was during a recital at the city dance hall in downtown Mitakihara. The mayor and a bunch of other bigwigs attended the event as a fundraiser for kids with cancer who could not afford treatment. Over a thousand people showed up and only five hundred could fit in the theater. After a few words of welcome from the mayor, the show began. The curtains parted, the ballerinas moved, and Charlotte opened her mouth.

Her voice! Oh, her voice! I thought my ears were fooling me at first. Then I thought that she had already been claimed by another one of me and that her wish was to possess the voice of an angel. She sang streams of silver. I felt these waves of energy emanate from her body. She poured her soul into those lyrics, and as I listened to her, I got a taste of just how powerful a Puella Magi she could be. I wasted no time approaching her and offering to make her a Puella Magi, but she refused. She came from a rich family and had everything she could possibly want. By age 12, she already owned a pony, the entire line of American Barbie dolls, and most importantly, she could eat whatever dessert or cheese she desired. Cakes, pies, cookies, pastries, cottage cheese, bleu cheese, you name it, she ate it. She was popular at school, she was at the top of her grade, her body was healthy, and she was modest. I couldn't possibly wish for anything, she told me. A true angel, I tell you. I could almost see the halo dangling above her head.

But I couldn't just let this opportunity pass by. That night, I visited little Charlotte in her room. She was sleeping, so I didn't have any trouble pulling a Grief Seed from my body and planting it beneath her bed. With any luck, the Grief Seed would absorb her negative emotions and eventually revive the witch within it.

Charlotte continued to thrive. For a year, she lived the life that many dream of but few experience. On Wednesdays and Fridays, she led the science club at her school. On Tuesdays and Thursdays, she participated in the school choir. On weekends, she sung for the church choir and was recognized nationally for her talent. And all the while, she kept on eating her desserts.

She applied to Mitakihara Middle School and gained admission. Not long after her first day of school, she came down with a terrible fever. No longer did she resemble the angel that she once was. Her once ruddy cheeks were now pale and stiff. Painful lumps sprouted on her neck and stomach. The doctors performed a blood test and revealed the tragic circumstances to her parents: Charlotte had leukemia. Her bones were producing white blood cells at a hasty rate, and without proper quality control, the cells were immature and could not function as proper protectors of her body. Pathogens could gain free entry into her body and destroy her as they pleased. Her parents were crestfallen. They placed her on an intensive regimen of daily chemotherapy followed by administration of a cocktail of anti-tumor agents. She was placed on a restricted diet. Fruits and vegetables, meats and protein, grain products; they were all fine. But she was not allowed to eat sweets or cheese, the two things she had loved so much. She snuck out of her bed a few times to ask for a slice of apple pie at the hospital's cafeteria, but the orderlies recognized her and sent her back to her room. After that, they kept the door locked.

She was resolute at first, but as months passed by, she grew increasingly hopeless. The cancer was killing her. Her jet black hair had fallen out, and she could barely talk let alone sing. All the while, she craved sweets and cheeses and lost her appetite for anything else. Her arms thinned out to the bones, and her eyes fell ashen.

By February, Charlotte looked like a skeleton dipped in wax. I knew that then was the best time to visit her. One night, I made my way to the medical center and perched on the windowsill to her room. On the stand beside her bed, The Very Hungry Caterpillar sat half-open.

"Psst!"

Charlotte slowly pulled open her eyelids. "You…."

"You're not looking so good. What happened?"

"Th-the doctors tell me it's acute leukemia. They have no idea how I came down with such a sudden case of it."

"Do you think you'll recover?"

"Neither the doctors nor my parents want to talk about it. They tell me to be strong. I figure that that means I probably won't make it."

"That's terrible! But I can help! You just have to make a contract with me."

She sat up in her bed and rubbed her eyes. Her movements were pained and sluggish. "I don't suppose I have any other choice."

"Just tell me your wish, and you'll be on your way."

"I…I just want to taste the sugar in my mouth again. I want to be able to eat as many desserts as I want."

"Ah! That can be done!"

The doctors later called it a miracle. They'd never seen anything like it. Charlotte had gone from the end stage of leukemia and made a full recovery. The red glow returned to her cheeks, and she regained her voice. Within a week, she was back in school and of course, savoring the taste of cake in her mouth. In her desperation, she forgot to add that she wanted to be able to eat cheese as well, but hey, what can I do? I'm just the messenger.

As a Puella Magi, Charlotte was the strongest one I had formed a contract with until I met you. You should have seen her. Her Soul Gem was an emerald that shone with the light of a million emotions. She had an unbelievable amount of talent, and as her skills were tempered by experience, she matured into an unstoppable fighter. Witches flinched at just the mention of her name, and other Puella Magi even paid tribute to her by bringing her cheese. Of course, she retained her love for sweets and never forgot to gobble down a dessert after every battle.

If you must know, she died battling the Walpurgis Night. The circumstances were similar to when you fought Walpurgis Night, except she didn't have any help. She held her own for a while, but the witch was just too strong. There's nothing more to it than that. She ran her course and as expected, became one of the strongest witches after her Soul Gem crumbled into a Grief Seed. All things said and done, she provided enough emotion for me to meet my quota for the next ten years! With her sacrifice, the universe was extended by 100 trillion years.

LIFE REQUIRES A SOURCE OF ENERGY. Energy can be used to do work, and work can reliably prevent local increases in entropy. In the case of Earth, your sun is that source of energy. It's just one big Soul Gem if you think about it. It throws its energy-rich rays at the Earth, and a small part of that energy gets used by plants and plankton. Those plants and plankton beget herbivores, and the herbivores beget carnivores. At the top of the pyramid lie human beings in all your biological glory. And for four and a half billion years, the sun steadily nourished the Earth with its heat drawn from the furnaces of nuclear fusion. Fueled by this energy, the forces of evolution combated the rise in entropy and over eons, prokaryotes evolved into eukaryotes, eukaryotes evolved into simple fish, simple fish evolved into tetrapods, tetrapods evolved into primates, and primates evolved into humans. This great chain of being remained unbroken for billions and billions of years, each organism passing on its genetic material onto its progeny until you, Madoka, were finally brought into this world. And all the while, the second law of thermodynamics chipped away at the very foundations of life. Every time a bacteria synthesized a protein, every time a cell replicated, entropy increased. That was okay though, because the sun continued to provide your planet will all the energy it ever needed to sustain itself.

You may not live to see it, but one day, your sun will run out of fuel and stop burning. From that point onward, entropy will inevitably rise. After an inordinate amount of time, every star will burn out, and the universe will homogenize. Once all of matter is evenly distributed across the universe, then entropy will cease to rise. That's because in this scenario, entropy is already at its maximum value, and the universe is in complete thermal equilibrium. No useful work can be done now, and life cannot possibly exist in such a thermodynamic hell. This is known as the heat death of the universe.

MITAKIHARA MIDDLE SCHOOL was the jewel of the Japanese school system. The 48,000 square meter campus consisted of six academic buildings, one administrative building, one health facility, and a state-of-the-art gym. Graduates regularly attended prestigious high schools and universities. The average score for a Mitakihara graduate on the college entrance examination is 301 (out of 400) compared to the national average of 234. The student-to-faculty ratio was the lowest of any middle school in the nation. Gaining admission to Mitakihara Middle School required scoring in the upper decile of the school's entrance exam, which covered all the subjects on the national college entrance exam. This is what Homura Akemi had read in the brochure that her parents brought her earlier today.

Homura folded up the brochure and placed it on the stand beside her hospital bed. She stretched, yawned, and looked outside. From the fourth floor of Mitakihara Medical Center, she could see for several miles out. Cars flowed on the streets like blood cells and eventually disappeared in the horizon where a row of apartment complexes stood. To the side of the road lay two baseball diamonds and four soccer fields. Children and adults alike routinely convened there to run, catch, kick, and sweat. Sports really did seem like fun.

The soft beep of the heart monitor next to the bed reminded her of her curse. She had been born with a disorder known as valvular heart disease. Normally, when your heart beats, valves open and close to prevent the backflow of blood. Homura's valves were damaged, so her heart was inefficient. If you place a stethoscope against the chest of a person with this disease, you can hear a distinct murmur that you wouldn't otherwise hear from a healthy patient. Because of her condition, Homura was confined to a bed and allowed only one daily half-hour walk around the hospital. If she performed any physical activity at all, her heart would scream and thrash. It would feel like there was a fireball in her chest.

Her well-to-do parents had paid for artificial heart valves to be implanted. When Homura heard that this would require opening up her chest, paralyzing her body, and cutting through cardiac tissue, her heart raced. The pain from that was unbearable, so she was forced to be brave. Her parents told her not to worry. These doctors were the best in the world.

She was to sit for the entrance exam at Mitakihara Middle School tomorrow. Her caretakers made an exception for her, but only this once. Since she was confined to a bed, she couldn't go to the mall or eat at a restaurant or visit the park like other girls her age did. She could only study and read books. Her parents had hired a cadre of tutors to provide her with a first class education from the bedside. They quickly discovered that despite all the physical handicaps that ailed her, she was blessed with a good mind. She gobbled up academic material and excelled in every subject that was presented to her. Her parents were pleased. The next day, she traveled to the testing center with the help of an aide and took the exam. She blazed through the English and history sections and had a bit or trouble on the math and science sections. A few guesses here and there, but nothing too serious. She was done a half-hour before time ran out and had the luxury of triple checking all of her answers while the rest of the students scribbled madly to finish. Scores would be out in a few days.

The next night, Homura underwent the operation. She didn't remember much besides the euphoria right before she went under. Men in procedure masks loomed above her all blurry and distorted. They carried scalpels and scissors and told her to relax. The monitors behind her made beeps and boops. She drifted into slumber even as the doctors shone a powerful light. It'll all be over in a second, they assured her.

When she opened her eyes, she was met with an endless expanse of black space. She looked around but could not find anything other than isotropic nothingness. Suddenly, a wall of fluorescence appeared above her and plunged down, slamming her into a ground that she hadn't noticed before. The darkness filled up with vibrant colors and strange shapes. They pulsated in steady beats and then slowed down to a halt. Blocks of brick thrust up and encased her in a tiny dome. Streams of red liquid seeped in from the cracks and then congealed into an amorphous blob. Two claws took shape and then two four legs and a head. The monster hissed and brandished its pincers. Homura screamed.

From above, a bolt of energy pierced the brick and blasted off one of the monster's legs. It stumbled backward and howled in pain. Homura looked up and spotted a shadowy figure perched by the edge of a hole in the dome. The figure's outline revealed a large dress and ribbons tied to each side of her hair. A pink oval glowed from her neck. She drew back a bow she carried, and another bolt of energy descended and struck the monster in its torso. Homura watched as it let out a final death cry and then shattered into shards of negative space.

"Wh-Who are you!" Homura called out to her savior, but she was already gone.

The colors around her turned into a hundred shades of red. They began to swirl in one great bloody vortex. Homura hugged herself to keep from quivering. From outside, a string of words exploded past the brick dome and rattled her eardrums.

Oh no. We're losing her.

The voice sounded familiar, but she couldn't tell for sure. The walls began to crumble.

Her heart's coming back too soon! We need some saline solution stat!

The whirlpool of red around her pulsed in booming thumps. She fell to her knees and clutched her chest. It felt like it was going to burst. Slowly, slowly, the vortex stopped spinning, and the red desaturated into gray, then the gray darkened into black. Homura hung in weightless silence once again. It was like being trapped in a sensory deprivation chamber.

In the operating room, the doctors scrambled to keep Homura alive. The ice around her heart melted too quickly, and it began to beat in the middle of a critical incision. The scalpel accidentally sheared through a delicate mass of cardiac tissue, and now the proposition that Homura may not wake up went from possible to probable. Her parents, who were watching from above, held their breaths. The surgeons' yelling and harried movements flustered her fragile mother. She turned red and cried. The husband and wife held each other and prayed for a miracle.

A MAN STANDS IN FRONT of a video camera with a tennis ball in his hand at chest height. The recording begins, and the man releases the ball. It accelerates toward the ground and hits it with a soft bop. The ball bounces off the ground and rises back into the man's hand. Now, take the footage and run it in reverse. If the conditions are right, the reversed clip will look the same as the forward clip. In other words, the laws of physics are time symmetrical; they are viable regardless of whether you run time forwards or backwards. Gravity is the same, momentum is the same, electromagnetism is the same, and so on. But there is one big difference between the two clips. In the forward clip, the ball reaches a lower maximum height after its bounce. This is because on its way down, the tennis ball loses energy to air resistance, to the ground when it bounces, and then more to air resistance on its way up. The ball can never gain this energy back. It cannot convert random vibrational energy (in other words, temperature) back into ordered kinetic energy (in other words, velocity). This would be a violation of the pesky second law of thermodynamics. See how annoying this can be?

If you observe chemical reactions on a nanoscopic scale, you wouldn't be able to tell which way time was flowing; everything looks feasible either way. But if you zoom out and study systems on a macroscopic scale, you'll see that disorder inevitably increases. A cloud of ink in water can never coalesce back into the original drop. It's fated to dissipate. You may get a few localized buildups of order here and there, but none serious enough to be labeled a violation of the second law. Because entropy reliably increases as time progresses, the arrow of time is a thermodynamic one. If we can reverse entropy, we can in effect, reverse time. Isn't that exciting?