  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.
