Fluctuation theorem for quantum-state statistics
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.
Cite
@article{arxiv.1807.11683,
title = {Fluctuation theorem for quantum-state statistics},
author = {Naoto Tsuji and Masahito Ueda},
journal= {arXiv preprint arXiv:1807.11683},
year = {2018}
}