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Thermodynamically-Efficient Local Computation: Classical and quantum information reservoirs and generators

The thermodynamics of modularity identifies how locally-implemented computation entails costs beyond those required by Landauer's bound on thermal computing. We prove a general theorem for efficient local computation, giving the necessary and sufficient conditions for a local operation to have zero modularity cost. Applied to thermodynamically-generating stochastic processes it confirms a conjecture that classical generators are efficient if and only if they satisfy retrodiction, which places minimal memory requirements on the generator. We extend this to quantum computation: any quantum generator that employs quantum memory compression cannot be thermodynamically efficient.