Many systems can be decomposed into a set of subsystems, where the dynamics of each subsystem only depends on some of the other subsystems rather than on all of them. Here I derive an infinite set of lower bounds on the entropy production of any such composite system, in terms of the initial distribution of its states, the ending distribution, and the dependencies of the dynamics of its subsystems. In contrast to previous results, these new bounds hold for arbitrary dependencies among the subsystems, not only for the case where the subsystems evolve independently. Moreover, finding the strongest of these new lower bounds is a linear programming problem. As I illustrate, often this maximal lower bound is stronger than the conventional Landauer bound, since the conventional Landauer bound does not account for the dependency structure.
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