Duvenhage, Rocco2025-07-072025-07-072025-092025*S2025http://hdl.handle.net/2263/103201https://doi.org/10.25403/UPresearchdata.29480738.v1Dissertation (MSc (Physics))--University of Pretoria, 2025.We develop quantum detailed balance on a finite-dimensional system in terms of elementary transitions, which are pure states on the composite space consisting of two copies of the system. This is in close analogy to detailed balance in classical mechanics described in terms of Markov chains. We show that this version of detailed balance may also be expressed in terms of quantum channels. acting on the states of the system by the Choi-Jamiolkowski duality. We then develop a more general setting of states and channels in a von Neumann algebraic framework and embed our theory of finite-dimensional elementary transition detailed balance into this framework. Lastly, we show that our version of quantum detailed balance is equivalent to the well-known standard quantum detailed balance with respect to a reversing operation in finite dimensions.en© 2024 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)Quantum detailed balanceQuantum channelsChannel-state dualityVon Neumann algebrasOperator algebrasDissertationu19128895https://doi.org/10.25403/UPresearchdata.29480738