  I consider multipartite processes in which there are constraints on each
subsystem's rate matrix, restricting which other subsystems can directly affect
its dynamics. I derive a strictly nonzero lower bound on the minimal achievable
entropy production rate of the process in terms of these constraints on the
rate matrices of its subsystems. The bound is based on constructing
counterfactual rate matrices, in which some subsystems are held fixed while the
others are allowed to evolve. This bound is related to the "learning rate" of
stationary bipartite systems, and more generally to the "information flow" in
bipartite systems.
