Information-theoretic bound on the energy cost of stochastic simulation

TL;DR

This paper establishes a fundamental lower bound on the energy required for stochastic simulation of physical systems, linking thermodynamics, information theory, and complexity through information measures.

Contribution

It derives the minimal energy cost of stochastic simulation based on the difference between statistical complexity and predictive information, connecting information erasure to thermodynamic cost.

Findings

Energy cost proportional to information erasure

Link between thermodynamics and information complexity

Illustration using Szilard engine Gedankenexperiment

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.