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Physical systems are often simulated using a stochastic computation wheredifferent final states result from identical initial states. Here, we derivethe minimum energy cost of simulating a complex data set of a general physicalsystem with a stochastic computation. We show that the cost is proportional tothe difference between two information-theoretic measures of complexity of thedata - the statistical complexity and the predictive information. We derive thedifference as the amount of information erased during the computation. Finally,we illustrate the physics of information by implementing the stochasticcomputation as a Gedankenexperiment of a Szilard-type engine. The resultscreate a new link between thermodynamics, information theory, and complexity.

Information-theoretic bound on the energy cost of stochastic simulation