Part V: Information & Physics
The Physical Basis of Information
Information is not merely an abstract concept — it has deep physical roots. The manipulation, storage, and erasure of information are constrained by the laws of thermodynamics. This part explores the profound connections between information theory and physics, from Maxwell's nineteenth-century thought experiment to the modern black hole information paradox.
Rolf Landauer's principle establishes that information erasure has an irreducible thermodynamic cost, while the Bekenstein-Hawking entropy reveals that black holes encode information on their event horizons — one bit per Planck area.
Chapters in This Part
Chapter 13: Maxwell's Demon
The thought experiment, Szilard engine, and the resolution via information theory — the demon must erase memory, paying entropy debt to the environment.
Chapter 14: Landauer's Principle
Erasing one bit of information requires at least \(k_B T \ln 2\) of energy. Derivation, experimental verification (2012), and reversible computing.
Chapter 15: Black Hole Information Paradox
Bekenstein-Hawking entropy, holographic principle, Hawking radiation, the Page curve, and recent resolution via islands and replica wormholes.
Key Equations
Landauer Limit: \( W_{\min} = k_B T \ln 2 \approx 2.85 \times 10^{-21} \text{ J at room temperature} \)
Bekenstein-Hawking Entropy: \( S_{BH} = \frac{k_B c^3 A}{4 G \hbar} = \frac{A}{4 \ell_P^2} \)
Szilard Engine Work: \( W = k_B T \ln 2 \) per measurement cycle