As there were lessons in the mornings and the afternoons, Alice had been taking her lunches with the Vallmont family, which included the Marquis, his wife, and their children.
On days when the Marchioness wasn't too busy, the Countess would join her daughter as her guardian and would have a tea party with the Marchioness.
At first, the Vallmonts tried to make small talk with Alice, but they eventually stopped and began asking her more specific questions about the lessons and magic. Alice suspected that Maximilian had told his parents at some point that small talk made her uncomfortable and that a more direct approach was better. Despite not liking the idea of needing protection from a child younger than herself, Alice was still grateful to Maximilian for the most part.

One day, Rachel and Alice were practicing sword fighting with wooden sticks, although it was more like playing than actual training. This was Rachel's idea, as she wanted them to play outside before Alice had her afternoon magic lesson. Rachel was very kind but easily excited about everything, although not for long. On Earth, she might have been diagnosed with some kind of hyperactivity disorder.
Despite Rachel's extroverted and energetic personality,  which should be Alice’s worst nightmare, she actually didn't mind too much. After all, Rachel always led conversations and, because she was always talking and asking things, Alice could simply ignore about half of the questions since Rachel would just get suddenly excited about something else entirely. Rachel was an easy-going girl who was not interested in the usual noble small talk in the slightest, and that was why Alice was comfortable with her.

"Come on, show me your magic!"
"I have told you multiple times that we should not do this without a practical magic instructor. I am not even sure you would find my magic that interesting anyway."
"It's fine, right? I'll just make you show me once so you don't use up all your mana. Show me your strengthening magic."
"Again, this is not strengthening magic since I do not power up my muscles. Though I might be able to mimic it."
"Just show me once! It's an order!"
"Ugh, alright. I will just throw a ball."
"No, I heard your throw looks pitiful. Hit the ball with the stick you're holding."
"P-pitiful? Who told you that?"
"It doesn't matter. Get your stick ready, I'll throw the ball at you!"
"Alright, but be careful with your throw. I will position myself with an angle so that I do not hit you. Please launch the ball in a parabola."
"Yeah, yeah. Get ready."

Somehow Rachel didn't seem to understand what a parabola was since she threw the ball straight with all her strength.

"Go!"

(A full-speed throw?! This isn't a parabola at all!)

Panicking, Alice swung her mana-powered stick and only grazed the ball: she had missed it.
Because of her strong build, Rachel had launched the ball with great momentum, at least compared to Alice's throws. Just before the ball hit her forehead, Alice saw a bright flash.

(Gaaaaaaah!!! Or not?)

Alice had hoped the impact wouldn't hurt too much, but she didn't actually expect it to be the case. It did sting a bit, but considering the weight and speed of this ball, Alice could not explain how it did so little to her face.
As such, she rapidly concluded that she somehow managed to deprive the ball of some of its kinetic energy, which was the exact opposite of what she had done before.
Thinking back, she suspected that, as the stick grazed the ball, some of the mana enveloping it had stuck to the ball and reacted to her thoughts just before the impact.

(So I can take off the kinetic energy too… But where did it go?)

The first law of Thermodynamics stated that energy could not be destroyed or created from nothing. It could only be converted into another form.
Before now, Alice had been making her mana act like a sort of potential energy that turned into kinetic energy upon contact with a target. This let her change the total amount of energy in a system in its current inertial frame of reference, without changing its force or even its momentum.
This time, however, the kinetic energy of the ball had seemingly decreased. Did this energy become something else, like heat? Alice thought she saw a light coming out of the ball just before receiving it in the face. Could that be it?

“W-what happened?! Are you okay? Why did my ball sparkle like that?”

(So I guess it wasn’t my life flashing before my eyes… Then, I suppose that I can convert kinetic energy into light too. I wonder if I’m able to convert it into other forms of energy.)

This was getting exciting. Maybe her element was not only restricted to kinetic energy after all.
But then, Alice made a hypothesis she definitely needed to try out as soon as she could.

(In the first place, since I can convert mana into kinetic energy, doesn’t it mean mana is de facto another form of energy according to Thermodynamics? Otherwise, the additional kinetic energy that I give to objects would break the first law…)

If energy was all about conversion, it made sense.
Not to mention, in this world, living beings recovered their mana with food. After all, the more mana mages had, the more they ate in a day.
It would then mean that they converted their food into chemical energy, then into mana, and then into another form of energy depending on their element while casting magic.

There was a good chance that Alice’s magic type was indeed broader than just the control of kinetic energy. It might be energy manipulation. So, if mana was really another form of energy, couldn’t she transform kinetic energy into mana, hence generating it just by taking a hit?

Alice gave Rachel a very noble-like smile.

“Shall we do it again, my Lady?”
“W-what? Are you mad at me or something?”

For once, Rachel was afraid of this little girl who had such an intense grin. The Marquis’ daughter hoped that Alice’s afternoon lessons would start soon.

***

By default, when Alice was enveloping something like a projectile with her mana, it was acting like potential energy that turned into kinetic energy later. However, there seemed to be some losses, probably because she was only a beginner.
Even ignoring the losses, however, she was sure to lose at the very least as much mana as the new kinetic energy she added to a projectile when she attacked, in joules-equivalent.
On the other hand, if she was hit by something carrying kinetic energy, instead, she had to use only a small quantity of mana to convert the attack into other things, like light or heat. This made defense much more efficient than offense in terms of preserving mana.
Moreover, if Alice was able to convert kinetic energy into mana, she might be able to have even more mana at her disposal than she had before being attacked. It sounded broken.

***

Well, it was true in theory. In the end, Alice had to mobilize a great deal of mana to catch the ball's kinetic energy. As it happened, the more mana density there was, the more kinetic energy was decreased. However, without knowing where the ball would hit, she had to increase the volume of mana in front of her. If she wanted to stop the ball at the very last moment before the impact, a consequent wager of mana was necessary.

"Uh... Alice, let's stop doing that. Look at you..."
"No, please continue throwing the ball! I feel like I am starting to get the gist of it! "
"..."

After some time, she had to resort to predicting where the ball would strike her in order to reduce as much as possible the amount of mana she mobilized. Her face might have been correctly covered, but she had to rely on her hands enveloped by mana to catch the projectile anywhere else. The issue was that she was not that great at analyzing the trajectory. The fact that Rachel was the one to suggest stopping spoke volumes about the number of failed attempts at catching the ball.

By the time her afternoon lesson started, she looked all beat up, dirty, and a little anemic due to her almost empty mana pool. Since she did not know how to reabsorb her own mana yet, she had left a lot over there.

“What happened to you?! Did my sister do this to you? Now she is going way too far!”
“No, it is quite alright! I was the one asking her to hit me!”
“... What? Are you an idiot? Or some kind of pervert?”

Maximilian looked at her in disgust. He regretted worrying about her. This afternoon, he decided it was best not to ask her any questions after the lesson.

Somehow, Alice seemed way more invested in the lesson than usual. It was about manipulating mana in a mage’s surroundings in order to perform magic at a distance. These techniques were especially useful for mages who would rather not touch their own magic, like ice, fire, or lightning mages. Since they too were at risk, they had to make their mana come out of their hand, stabilize it around them, and only then turn the mana into magic. For mages who could touch their magic, however, like earth or water mages, it was not as useful. Still, even these mages could use this technique to attack from behind their target at close range.
Another part of the lesson was about how to reabsorb the mana while it had not been transformed into magic yet. It was apparently a thing that was made possible by a combination of breathing techniques and a clear visualization of the mana flowing in the opposite direction toward the body. Maximilian did not really get all of this, but Alice seemingly did as she had been nodding constantly for about three minutes.

This kind of lesson about the magic system was just as important as the ones about the physical phenomena that magic types were based on. Having a good understanding of how mana could flow through the body and its surroundings could increase the likelihood of an individual awakening an element that was optimized for their mana flow.

As such, Maximilian was wondering how Alice could use this knowledge as both an already awakened kid and a pseudo-strengthening mage at that. It was clearly too late to change how her mana flowed in her veins, and the idea of strengthening mages manipulating mana outside their bodies was stupid in the first place. Yet, for some reason, she seemed very invested in the lesson. She was even writing verbatim everything the instructor was saying, which made the latter pretty uncomfortable.

By the time the afternoon lesson ended, Maximilian realized he had completely given up listening to the tutor, and instead had been thinking about Alice’s magic. Since she paid attention, at least, she would probably explain to him what he missed. It was her role in the first place, anyway.
When they left the room he chose to ask her, even though he had planned to ignore her for the day.

“Say, Alice, what did the tutor mean when he-”
“Sorry, I am busy! See you!”

That was what she immediately answered before running quite fast considering her small build.
Maximilian grumbled to himself as he watched Alice's retreating figure. It was rare for her to be such an open book, and he couldn't help but wonder what had her in such a hurry. He made a mental note to ask her about it later and decided to head back to his own room for the time being.

“... What a weirdo.”

***

There was no one practicing at the training ground, so Alice was alone. As such, she decided to put into practice everything she had just learned. She did not want to waste time because she would soon have to go back to the Ravendalls’ mansion in about an hour.

(If I don’t have the time to convert kinetic energy into mana when it starts making contact with my skin, maybe I can just start the process before then!)

It was possible to use and manipulate mana in a diameter of a few meters around the caster. As such, she probably could form a sort of cloud of mana that a ball or another object would have to pass through to get to her. Then, she would be able to begin the conversion before it touched her. By the time the object would eventually make contact with her, it would theoretically have almost no energy left. Moreover, she would be controlling both the newly created mana and her own clump of mana, minus the part that would have been consumed for the conversion.
From then, she would either reconvert the mana into another form of energy like heat, light, or kinetic energy, or she would reabsorb it all to fill up her mana pool.

Mana was pretty mysterious. In the world of her former self, it had never been detected, even though it was everywhere in this world. All species, be they animal or vegetal, were producing mana. Plants and trees even emitted mana along with oxygen during their photosynthesis. It was an invisible energy that every being could feel and that had a unique signature for each individual. Magic, on the other hand, was the bending of reality according to a mage’s element through the medium of mana.
If Alice managed to find a way to bend reality to end up with more mana than what she had before casting her magic, this would be a first in this world. Frankly, she was unsure about sharing this with other people, as it sounded like a good reason to be targeted by some powerful nobles.

(Wait, I’m alone… Who will throw a ball at me? Should I have asked Maximilian? Well, now that I’m here, I’ll just start manipulating at a distance the mana I have left in my mana pool, and try reabsorbing it. That’s too bad, but I’ll have to produce mana another day.)

She made her mana leave her hands and made it float around her in an invisible orbit. It was a bit of mental gymnastics at first, but she managed to get used to it in a few minutes.

(Manipulating mana in the air... That's truly a game changer.)

Then she tried absorbing back the mana that she had been manipulating, and she managed to do it the third time. As it happened, the breathing part of this technique was more important than Alice thought. But now, thanks to that, she would be able to reabsorb all the mana she was constantly and involuntarily emitting. In her mansion, her bedroom was so saturated with her mana that all the maids who entered felt chills every time. For now, she filled her mana pool with the mana that had been left here when she trained with Rachel earlier. She decided that she would do the same thing at her mansion as soon as she would return there.

Then, she tried converting small parts of the big cloud of mana in front of her into light and heat, and she succeeded.
Since she was only a beginner at magic, her energy conversions had significant losses in energy, in the form of heat. When she converted in one go a certain volume of mana, about 20% of it was lost while 80% of it was converted into another form of energy.
Still, even without much training, she was already converting energy with an 80% efficiency. Compared to this, photosynthesis converted only about 2% of light into chemical energy, while the conversion of the chemical energy in food into mechanical energy by animals was thought to be about 20% efficient.
Thus, her measly 80% efficiency made those conversions one of the most efficient in this world.
Frankly, she would probably never get to a full 100% efficiency because of the second law of Thermodynamics. In a closed system, there were always some losses during energy conversions, since entropy could not decrease in a system.

(That’s all well and good, but if we’re talking about the purest conversion in the universe, it has to be annihila-)

Just as she was casually thinking while still actively manipulating her mana in the air, Alice interrupted her train of thought as she felt her right hand trembling for some reason. She had a look at it and followed the thin trace of mana. In a minuscule section of the cloud she had been controlling, the mana density was not right: the numbers did not add up. An expression of fear appeared on her face as she had a realization and, an instant later, there was an explosion.