Duvenhage, Rocco2025-01-152025-01-152025-042024-11*A2025http://hdl.handle.net/2263/100072Thesis (PhD (Physics))--University of Pretoria, 2024.We develop a general framework for studying classes of quantum dynamical systems that are close to and structurally similar to other systems satisfying specified properties, in particular, quantum detailed balance conditions. This is done in terms of optimal transport plans and Wasserstein distances between systems on possibly different observable algebras. Basic metric properties of Wasserstein distances are proven. As a possible application of our framework to non-equilibrium statistical mechanics, bounds on deviations from detailed balance are derived.en© 2023 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.UCTDSustainable Development Goals (SDGs)Wasserstein distancesOptimal transportQuantum detailed balanceBimodulesTomita-Takesaki theoryThesisu1004952610.25403/UPresearchdata.28060394