Information processing typically occurs via the composition of modular units,such as universal logic gates. The benefit of modular information processing,in contrast to globally integrated information processing, is that complexglobal computations are more easily and flexibly implemented via a series ofsimpler, localized information processing operations which only control andchange local degrees of freedom. We show that, despite these benefits, thereare unavoidable thermodynamic costs to modularity---costs that arise directlyfrom the operation of localized processing and that go beyond Landauer'sdissipation bound for erasing information. Integrated computations can achieveLandauer's bound, however, when they globally coordinate the control of all ofan information reservoir's degrees of freedom. Unfortunately, globalcorrelations among the information-bearing degrees of freedom are easily lostby modular implementations. This is costly since such correlations are athermodynamic fuel. We quantify the minimum irretrievable dissipation ofmodular computations in terms of the difference between the change in globalnonequilibrium free energy, which captures these global correlations, and thelocal (marginal) change in nonequilibrium free energy, which bounds modularwork production. This modularity dissipation is proportional to the amount ofadditional work required to perform the computational task modularly. It hasimmediate consequences for physically embedded transducers, known asinformation ratchets. We show how to circumvent modularity dissipation bydesigning internal ratchet states that capture the global correlations andpatterns in the ratchet's information reservoir. Designed in this way,information ratchets match the optimum thermodynamic efficiency of globallyintegrated computations.
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