Fluctuation Theorem for Many-Body Pure Quantum States

Thermodynamics of quantum systems has attracted much attention in light of the development of modern theories and the state-of-the-art experimental technologies. Especially, it has been established that the second law of thermodynamics is a direct consequence of the fluctuation theorem. However, the standard approach of quantum thermodynamics is based on the canonical ensemble, and the second law for pure quantum states is yet to be understood. In the present work [1], we have proved the second law and the fluctuation theorem for pure quantum states in the short time regime. In our setup, the entire system obeys unitary dynamics, where the initial state of the heat bath is a single energy eigenstate that satisfies the eigenstate-thermalization hypothesis. Our proof is mathematically rigorous, where the Lieb-Robinson bound plays a crucial role. We confirmed our theory by numerical simulation of hard-core bosons, and observed the dynamical crossover from thermal fluctuations to bare quantum fluctuations. Our result would reveal a universal scenario that the second law emerges from quantum mechanics.
[1] E. Iyoda, K. Kaneko, and T. Sagawa, PRL 119, 100601 (2017).