Quantum 2025 – wissenschaftliches Programm

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THU: Thursday Contributed Sessions

THU 2: Quantum Information: Concepts and Methods I

THU 2.1: Vortrag

Donnerstag, 11. September 2025, 14:15–14:30, ZHG002

Concentration of ergotropy in many-body systems — •Karen Hovhannisyan¹, Rick P. A. Simon^{2, 1}, and Janet Anders^{1, 2} — ¹University of Potsdam, Institute of Physics and Astronomy, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany — ²Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, UK

Ergotropy---the maximal amount of unitarily extractable work---measures the ``charge level'' of quantum batteries. We prove that in large many-body batteries ergotropy exhibits a concentration of measure phenomenon. Namely, the ergotropy of such systems is almost constant for almost all states sampled from the Hilbert--Schmidt measure. We establish this by first proving that ergotropy, as a function of the state, is Lipschitz-continuous with respect to the Bures distance, and then applying Levy's measure concentration lemma. In parallel, we showcase the analogous properties of von Neumann entropy, compiling and adapting known results about its continuity and concentration properties. Furthermore, we consider the situation with the least amount of prior information about the state. This corresponds to the quantum version of the Jeffreys prior distribution---the Bures measure. In this case, there exist no analytical bounds guaranteeing exponential concentration of measure. Nonetheless, we provide numerical evidence that ergotropy, as well as von Neumann entropy, concentrate also in this case.

Keywords: ergotropy; quantum thermodynamics; concentration of measure; quantum batteries; many-body systems