Our aim is twofold: First, we rigorously analyse the generators of quantum-dynamical semigroups of thermodynamic processes. We characterise a wide class of gksl-generators for quantum maps within thermal operations and argue that every infinitesimal generator of (a one-parameter semigroup of) Markovian thermal operations belongs to this class. We completely classify and visualise them and their non-Markovian counterparts for the case of a single qubit. Second, we use this description in the framework of bilinear control systems to characterise reachable sets of coherently controllable quantum systems with switchable coupling to a thermal bath. The core problem reduces to studying a hybrid control system (“toy model”) on the standard simplex allowing for two types of evolution: (i) instantaneous permutations and (ii) a one-parameter semigroup of $d$-stochastic maps. We generalise upper bounds of the reachable set of this toy model invoking new results on thermomajorisation. Using tools of control theory we fully characterise these reachable sets as well as the set of stabilisable states as exemplified by exact results in qutrit systems.

我们的目标有两个：首先，我们严格分析热力学过程的量子动力学半群的生成元。我们描述了一大类gksl-热操作中量子映射的生成器，并认为马尔可夫热操作（的单参数半群）的每个无穷小生成器都属于此类。对于单个量子比特的情况，我们将它们和它们的非马尔可夫对应物完全分类和可视化。其次，我们在双线性控制系统的框架中使用此描述来表征可到达的相干可控量子系统集，这些系统具有与热浴的可切换耦合。核心问题简化为在标准单纯形上研究混合控制系统（“玩具模型”），允许两种类型的进化：（i）瞬时排列和（ii）单参数半群$d$-随机地图。我们概括了该玩具模型的可达集的上限，并调用了关于热重化的新结果。使用控制理论工具，我们充分描述了这些可达集以及可稳定状态集的特征，如 qutrit 系统中的精确结果所示。