"Youth has high entropy, doesn't it?"
Riku said out of nowhere.
"What do you mean?" Yuki asked back.
Aoi looked interested. "Try explaining."
"Well, you don't know what'll happen. Like what tomorrow brings."
"True," Aoi nodded. "Entropy is a measure of uncertainty. When you're young, there are many future choices."
Yuki began to understand. "More choices means higher entropy?"
"Yes. If n choices are equally probable, entropy is log₂(n) bits."
Riku calculated. "If there are 100 career paths, about 6.6 bits?"
"Correct. But if the probabilities are skewed?"
"Entropy decreases," Aoi explained. "For example, if there's a 90% probability of choosing one path, uncertainty is low."
Yuki thought. "So as you become an adult, entropy decreases?"
"You could say that. Choices narrow down, predictability increases."
Riku objected. "But isn't that boring?"
"Can't say that generally," Aoi answered carefully. "Low entropy means stability."
"Stability equals boring?"
"Not necessarily. If it's a path you chose yourself, even low entropy can be fulfilling."
Yuki wrote in her notebook. "Entropy = degrees of freedom?"
"Close. But too much freedom is also a problem."
"What do you mean?" Riku asked.
"Maximum entropy state is uniform distribution. Any choice is the same."
"Isn't that the same as not being able to choose?"
"Exactly," Aoi acknowledged. "True freedom exists within moderate constraints."
Yuki gave an example. "Like multiple choice questions on tests?"
"Good example. With 4 choices, entropy is 2 bits. But with knowledge, choices narrow down."
"By obtaining information, entropy decreases."
"Precisely. Learning is the process of reducing entropy."
Riku had a thought. "So we're reducing our youth entropy right now?"
"Might be," Aoi smiled. "By accumulating experience, the path forward becomes visible."
"But I don't want it completely zero."
"Why?" Yuki asked.
"Because there'd be no surprises. If everything's predictable, it's boring."
Aoi nodded deeply. "That's the beautiful part of information theory. Zero entropy is a state with no new information."
"No sense of being alive."
"Right. So life needs moderate uncertainty."
Yuki said, "Maybe youth is a time to enjoy entropy."
"Good interpretation," Aoi acknowledged. "Accept future uncertainty as possibility."
Riku laughed. "What if I graduate with high entropy?"
"That would be an interesting life in itself."
"But I want to reduce it a bit. At least decide on a career path."
Aoi started calculating. "Say you have 100 choices now, and narrow to 10, entropy decreases by about 3.3 bits."
"That's quite a reduction."
"It's called information gain. How much entropy decreased by obtaining new information."
Yuki summarized. "Youth is continuous information gain."
"Poetic," Aoi smiled.
Riku looked outside the window. "How many bits is our youth entropy right now?"
"Can't measure it, but we can feel it."
"Is it high?"
"I think it's high. But that's good."
The three nodded. Youth entropy. Precisely because it's high, every day is filled with new information.