Information-theoretic lower bound on energy cost of stochastic computation

Abstract

Physical systems are often simulated using a stochastic computation where different final states result from identical initial states. Here, we derive the minimum energy cost of simulating a data sequence of a general physical system by stochastic computation. We show that the cost is proportional to the difference between two informationtheoretic measures of complexity of the data-the statistical complexity and the predictive information. We derive the difference as the amount of information erased during the computation. Finally, we illustrate the physics of information by implementing the stochastic computation as a Gedanken experiment with a Szilard-type engine. The results create a new link between thermodynamics, information theory and complexity. © 2012 The Royal Society.