Minimum entropy production in multipartite processes due to neighborhood constraints
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It is known that the minimal total entropy production (EP) generated during the discrete-time evolution of a composite system is nonzero if its subsystems are isolated from one another. Minimal EP is also nonzero if the subsystems jointly implement a specified Bayes net. Here I extend these discrete-time results to continuous time, and to allow all subsystems to be simultaneously interacting. To do this I model the composite system as a multipartite process, subject to constraints on the overlaps among the "neighborhoods" of the rate matrices of the subsystems. I derive two information-theoretic lower bounds on the minimal achievable EP rate expressed in terms of those neighborhood overlaps. The first bound is based on applying the inclusion-exclusion principle to the eighborhood overlaps. The second is based on constructing counterfactual rate matrices, in which all subsystems outside of a particular neighborhood are held fixed while those inside the neighborhood are allowed to evolve. This second bound involves quantities related to the "learning rate" of stationary bipartite systems, or more generally to the "information flow".
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