"Why does entropy keep increasing?"
Yuki asked Aoi. Autumn sunlight streamed through the club room window.
"The second law of thermodynamics. In an isolated system, entropy never decreases," Aoi opened their notebook.
"But why?"
"It's a matter of the number of states. For example, there are overwhelmingly more ways for a room to be messy than organized."
Yuki looked around. Indeed, the club room was a bit messy.
"An organized state is one or a few. But there are countless ways to be messy. So when left alone, things naturally move toward disorder."
"It's a probability problem."
"Yes. Entropy is proportional to the logarithm of the number of microstates. S = k ln(W). Boltzmann's equation."
Aoi wrote the equation on the whiteboard.
"The larger W, the larger the entropy."
"So when we organize things, we're going against entropy?"
"Sharp question," Aoi smiled. "But when humans organize, we use energy through metabolism. In that process, the entropy of our surroundings increases."
"So overall, it's still increasing?"
"Exactly. The entropy of the entire universe is always increasing."
Yuki pondered. "Then someday the universe will reach maximum entropy and..."
"Called heat death. Everything becomes uniform temperature, and nothing more happens."
"That's scary."
"But it's billions of years away," Aoi said quietly.
While writing calculations in her notebook, Yuki suddenly realized something.
"Senpai, entropy is also used in information theory, right?"
"Yes. Shannon entropy. H(X) = -Σ p(x) log p(x). The form is similar, but the meaning is slightly different."
"How is it different?"
"Thermodynamic entropy is physical disorder. Information-theoretic entropy is the degree of uncertainty or surprise."
"But essentially the same?"
"Connected at the root. Both measure 'the number of possibilities.'"
Aoi looked out the window.
"In information theory too, there's a limit to data compression. Entropy is the lower bound."
"Can't reduce it?"
"Not without loss. This is also a kind of 'law.'"
Yuki chuckled softly. "Everything either keeps increasing or can't be reduced."
"Living within constraints might be nature's providence."
Silence flowed for a while.
"Senpai," Yuki said in a small voice. "Can feelings of love also be uncontrollable, like entropy?"
Aoi looked at Yuki in surprise.
"Suddenly, what..."
"No, it's just... my feelings grow on their own, and I can't organize them."
Aoi's expression softened.
"Entropy increases. Emotions too—the more you try to suppress them, the more complex they might become."
"Then what should I do..."
"Overall increase is inevitable. But within that, you can choose the important parts and organize the rest. That might be what living means."
Yuki nodded. "Like coexisting with entropy."
"Yes. Complete control is impossible. But you can face it."
The sunset dyed the club room orange.
"Thank you, senpai."
"Entropy keeps increasing," Aoi said quietly. "But there's beauty in that process. Love might be the same."
Yuki smiled. Today too, she learned something new. About entropy, and a little bit about her own feelings.