Thermodynamic speed limits for multiple, co-evolving systems

The thermodynamic speed limit theorems (SLTs) provide lower bounds on the time required for a system to evolve between any two given distributions, in terms of the system's total entropy production along the path with which its distribution evolves. Previously derived versions of the SLTs apply to a single physical system without regard to its internal structure. However, many systems of interest are multipartite, comprising a set of co-evolving subsystems. Here we derive three strengthened versions of the SLT that reflect the multipartite nature of such systems. The first is guaranteed to be at least as strong as the conventional "global" SLT. While the other two do not always have this guarantee, in many cases they are stronger than the first of our new SLTs. We demonstrate our results with a numerical example involving a cell sensing its environment.