Stochastic thermodynamics of co-evolving systems - beyond multipartite processes

A multipartite process (MPP) is a set of variables jointly evolving according to a continuous-time Markov chain for which only one variable can change its state at any time. Recent research in stochastic thermodynamics has produced a rich body of results concerning MPPs, highlighting the important role played by the network specifying which variable's value can directly affect the dynamics of which other variables. However, in many real systems multiple variables can change simultaneously, and so these systems cannot be modeled as MPPs. Indeed, some systems contain variables that cannot change state without a simultaneous change to some other variable's state. Examples of such "composite systems" range from molecule-level models of chemical reaction networks to electron-level models of circuits. Here, we analyze the stochastic thermodynamics of composite systems. Specifically, we derive novel decompositions of the entropy production and information flows for composite systems, based on the hypergraph specifying which variables are allowed to change state simultaneously. We also show how the hypergraph of a composite system can be used to strengthen thermodynamic bounds. In particular, we derive a tighter thermodynamic speed limit theorem, which suggests that given a fixed amount of dissipation, network structural constraints tend to cost extra time for evolution.