Fluctuation theorem for quantum-state statistics

TL;DR

This paper derives a fluctuation theorem for quantum-state statistics, linking forward and backward process data to free-energy differences, and explores system-size scaling differences between integrable and chaotic quantum systems.

Contribution

It introduces a new fluctuation theorem for quantum-state statistics that generalizes existing theorems and connects to out-of-time-order fluctuation-dissipation relations.

Findings

Quantum-state statistics relate to free-energy differences via an infinite series.

The theorem encompasses quantum work fluctuation theorem as a special case.

System-size scaling differs between integrable and chaotic systems, shown numerically.

Abstract

We derive the fluctuation theorem for quantum-state statistics that can be obtained when we initially measure the total energy of a quantum system at thermal equilibrium, let the system evolve unitarily, and record the quantum-state data reconstructed at the end of the process. The obtained theorem shows that the quantum-state statistics for the forward and backward processes is related to the equilibrium free-energy difference through an infinite series of independent relations, which gives the quantum work fluctuation theorem as a special case, and reproduces the out-of-time-order fluctuation-dissipation theorem near thermal equilibrium. The quantum-state statistics exhibits a system-size scaling behavior that differs between integrable and non-integrable (quantum chaotic) systems as demonstrated numerically for one-dimensional quantum lattice models.