Fluctuation Theorem for Many-Body Pure Quantum States

TL;DR

This paper proves the second law of thermodynamics and the fluctuation theorem for pure quantum states in many-body systems, establishing a rigorous link between quantum entanglement and thermodynamics, with potential experimental tests.

Contribution

It provides a mathematically rigorous proof of thermodynamic laws for pure quantum states obeying ETH, using Lieb-Robinson bounds and connecting entanglement entropy to heat.

Findings

Confirmed the fluctuation theorem for pure quantum states through numerical simulation.

Observed a crossover from thermal to quantum fluctuations in dynamical evolution.

Established a universal quantum scenario for the emergence of the second law.

Abstract

We 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-Robinson bound, which gives the upper bound of the velocity of information propagation in many-body quantum systems. The entanglement entropy of a subsystem is shown connected to thermodynamic heat, highlighting the foundation of the information-thermodynamics link. We confirmed our theory by numerical simulation of hard-core bosons, and observed dynamical crossover from thermal fluctuations to bare quantum fluctuations. Our result reveals a universal scenario that the second law emerges from quantum mechanics, and can experimentally be tested by artificial isolated quantum systems such as ultracold atoms.