Quantum Dynamical Entropy and Dissipative Information Flows
arXiv:2603.14025
Abstract
The Alicki-Lindblad-Fannes dynamical (ALF) entropy measures the rate at which new information is gathered about a quantum system by inspecting its long-time evolution. We propose an extension of the ALF entropy to open quantum dynamics as a measure of back-flow of information from the environment. Such a proposal is stronger than the existing ones based only on the open system reduced dynamics. In the case of a qubit collisionally coupled to a classical spin chain, we obtain an exact expression for the explicitly depending on the environment correlations. An extreme case shows how the information flow from environment to system corresponds to vanishing entropy production as for reversible finite quantum systems.
6 pages, 2 figures; see also the companion paper arXiv:2603.14015