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I consider multipartite processes in which there are constraints on eachsubsystem's rate matrix, restricting which other subsystems can directly affectits dynamics. I derive a strictly nonzero lower bound on the minimal achievableentropy production rate of the process in terms of these constraints on therate matrices of its subsystems. The bound is based on constructingcounterfactual rate matrices, in which some subsystems are held fixed while theothers are allowed to evolve. This bound is related to the "learning rate" ofstationary bipartite systems, and more generally to the "information flow" inbipartite systems.

Minimal entropy production due to constraints on rate matrix dependencies in multipartite processes