Fluctuation Theorem for Many-Body Pure Quantum StatesWe prove the second law of thermodynamics and the nonequilibirum fluctuation theorem for pure quantum states.The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but is a single energy-eigenstate that satisfies the eigenstate-thermalization hypothesis (ETH). Our result is mathematically rigorous and based on the Lieb-Robins
