The dependence on finite reserves of raw materials and the production of waste are two unsolved problems of the traditional linear economy. Healthcare, as a major sector of any nation, is currently facing them. Hence, in this paper, we report theoretical and practical advances of robotic reprocessing of small medical devices. Specifically, on the theory, we combine compartmental dynamical thermodynamics with the mechanics of robots to integrate robotics into a system-level perspective, and then, propose graph-based circularity indicators by leveraging our thermodynamic framework. Our thermodynamic framework is also a step forward in defining the theoretical foundations of circular material flow designs as it improves material flow analysis (MFA) by adding dynamical energy balances to the usual mass balances. On the practice, we report on the on-going design of a flexible robotic cell enabled by deep-learning vision for resources mapping and quantification, disassembly, and waste sorting of small medical devices.