Entropy

Abstract This chapter explores irreversibility, disorder, and ignorance as manifestations of entropy. Entropy measures irreversibility. The inevitable increase of entropy was discovered by analyzing a reversible heat engine, and implied the heat death of the Universe. Entropy measures disorder. Osmotic pressure is the entropy of ions in water; the residual entropy of glasses measures their atomic disorder. Entropy measures our ignorance about the world. Information entropy is used to compress messages and files on the Internet. Exercises span information entropy (burning information and Maxwell’s demon, reversible computation, card shuffling, Shannon entropy, entropy of DNA and aging, entropy of messy bedrooms, data compression), fundamentals of equilibration (Arnol’d cat map, proofs for and against entropy increase, phase conjugate mirrors), materials science (rubber bands and glasses), and astrophysics and cosmology (life at the end of the Universe, black hole entropy, Dyson spheres, cosmic nucleosynthesis and the arrow of time).