  Modularity dissipation identifies how locally-implemented computation entails
costs beyond those required by Landauer's bound on thermodynamic computing. We
establish 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. This extends immediately to quantum computation: Any quantum
simulator that employs quantum memory compression cannot be thermodynamically
efficient.
