Information-theoretic bound on the energy cost of stochastic simulation

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 complex data set of a general physical system with a stochastic computation. We show that the cost is proportional to the difference between two information-theoretic 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 Gedankenexperiment of a Szilard-type engine. The results create a new link between thermodynamics, information theory, and complexity.

5 pages, 1 figure

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• Thermodynamics of complexity and pattern manipulation
• Unbounded memory advantage in stochastic simulation using quantum mechanics
• Towards Quantifying Complexity with Quantum Mechanics
• Optimal high-level descriptions of dynamical systems
• The fundamental thermodynamic bounds on finite models
• Measuring complexity
• A computational mechanics approach to estimate entropy and (approximate) complexity for the dynamics of the 2D Ising Ferromagnet