entropy

A measure of the number of microscopic configurations consistent with a macroscopic state — quantifying disorder and missing information theory.

• second law of thermodynamics: entropy of an isolated system never decreases
• defines the arrow of time: the direction in which entropy increases
• Boltzmann entropy: S = k_B ln W, where W is the number of accessible microstates
• Shannon entropy: the information-theoretic analog — measures uncertainty in bits, bridging physics and information theory
• maximum entropy at thermal equilibrium — see temperature and thermodynamics
• black hole entropy (Bekenstein-Hawking): proportional to horizon area, linking gravity, quantum mechanics, and information theory
• free energy = energy minus temperature times entropy — governs spontaneous processes
• low-entropy initial conditions of the universe are a central puzzle in cosmology