  Previously derived "global" thermodynamic speed limit theorems state that
increasing the maximum speed with which a system can evolve between two given
probability distributions over its states requires the system to produce more
entropy in its evolution. However, these theorems ignore that many systems are
not monolithic, but instead comprise multiple subsystems that interact
according to an (often sparse) network. Indeed, most naturally-occurring and
human-engineered systems of increasing complexity can be decomposed into sets
of co-evolving subsystems, where there exist a priori constraints on the
dynamics of each subsystem, restricting which other subsystems can affect its
dynamics. Here we derive three new SLTs that account for the thermodynamic
effects of such constraints. Our first new speed limit strengthens the global
speed limit. While our other two SLTs do not have this guarantee, in some
situations they are even stronger than our first speed limit. Our results
establish that a stochastically evolving system will, on average, produce more
entropy in evolving between two distributions within a given time simply due to
its comprising multiple, co-evolving subsystems. We illustrate our results with
numerical calculations involving a model of two cells sensing and storing
information about their environment.
