"Does information have weight?"
Yuki suddenly asked. The three were studying in the library.
Aoi looked up with interest. "Physical weight?"
"Not as a metaphor. Really."
"Interesting question. The answer is, in a sense, yes."
Riku was confused. "Information is heavy? Data has mass?"
At that moment, Professor S. passed by.
"Good discussion. The physical aspect of information."
"Professor, does information have weight?" Yuki asked.
"No direct mass. But holding information requires physical states. And matter and energy are equivalent."
Professor S. sat down.
"E=mc². Einstein's equation. Energy is equivalent to mass. And processing information requires energy."
Aoi supplemented. "Landauer's principle. Erasing 1 bit of information requires at least kT ln2 energy."
"Erasing?" Riku asked.
"Yes. Storing information requires no energy in principle. But erasing always requires energy."
Professor S. continued explaining. "Write information to memory. Eventually, it fills up. Old information must be erased."
"That's when energy is needed?" Yuki confirmed.
"Needed. And that energy is released as heat."
"That's why computers get hot," Riku understood.
"Partly. Computation itself requires no energy if reversible. But information erasure is irreversible and always produces heat."
Aoi calculated. "Erasing 1 bit at room temperature is about 3×10⁻²¹ joules."
"Incredibly small," Riku said.
"Yes. But modern computers process trillions of bits per second. It accumulates to significant energy."
Yuki thought. "So if information increases, universe's energy decreases?"
"Opposite," Professor S. corrected. "When information is erased, entropy increases. The universe tends toward disorder."
"But if we store information?"
"Storage itself requires no energy. But maintenance requires fighting noise. That uses energy."
Aoi presented a new perspective. "Considering black hole entropy, information has physical reality."
"Black holes?" Riku was surprised.
"Black hole entropy is proportional to surface area. Related to amount of information contained inside."
Professor S. nodded. "Bekenstein-Hawking formula. Information is inscribed in space."
"Inscribed in space..." Yuki murmured.
"Yes. Information isn't an abstract concept, but part of the physical universe."
Riku asked. "So books in this library are heavier? Because they're full of information?"
"Strictly speaking, yes," Professor S. smiled. "But the difference is too small to measure."
Aoi supplemented. "Theoretically, having information defines the system's energy state. If there's energy, there's mass."
"But practically negligible," Professor S. said. "Mass change is less than trillionths of an electron's mass."
Yuki looked at her notebook. "Information theory is really physics."
"It is. Information, matter, and energy are inseparable."
Riku joked. "So when studying makes your head heavy, it's the weight of information?"
"That's fatigue," Aoi laughed. "But it's true the brain consumes energy."
"The brain is only 2 percent of body mass but uses 20 percent of energy," Professor S. taught.
"Most of that is used for information processing."
Yuki looked out the window. "I feel like this entire universe is made of information."
"Some physicists argue that," Professor S. said quietly. "It from bit. All physical reality arises from information."
"Philosophical," Riku said.
"The frontier of information theory is at the boundary of philosophy and physics," Aoi answered.
The four continued quietly reading books, feeling the invisible weight of information. With each bit of knowledge gained, information is written, erased, and energy flows in the brain.
Information may appear light, but might actually be the foundation of the universe.