  Many dynamical systems consist of multiple, co-evolving subsystems (degrees of freedom). These subsystems often depend upon each other in a way that restricts the overall system's dynamics. How does this network of dependencies affect the system's thermodynamics? Prior studies in the stochastic thermodynamics of multipartite processes (MPPs) have approached this question by restricting the system to allow only one subsystem to change state at a time. However, in many real systems, such as chemical reaction networks or electronic circuits, multiple subsystems must change state together. Therefore, studies of MPPs do not apply to such systems. Here, we investigate the thermodynamics of composite processes, in which subsets of subsystems are allowed to change state simultaneously. These subsets correspond to the subsystems that interact with a single mechanism (e.g., a thermal or chemical reservoir) that is coupled to the system. An MPP is simply a (subcase of a) composite process in which all such subsets have cardinality one. We demonstrate the power of the composite systems framework to study the thermodynamics of multiple, co-evolving subsystems. In particular, we derive thermodynamic uncertainty relations for information flows in composite processes. We also derive strengthened speed limits for composite processes. Our results apply to a much broader class of dynamical systems than do results for MPPs, and could guide future studies of the thermodynamics of distributed computational systems. 
Stochastic thermodynamics of multiple co-evolving systems -- beyond   multipartite processes