TY - JOUR

T1 - Information-theoretic lower bound on energy cost of stochastic computation

AU - Wiesner, Karoline

AU - Gu, Mile

AU - Rieper, Elisabeth

AU - Vedral, Vlatko

PY - 2012/12/8

Y1 - 2012/12/8

N2 - 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 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 Gedanken experiment with a Szilard-type engine. The results create a new link between thermodynamics, information theory and complexity.

AB - 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 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 Gedanken experiment with a Szilard-type engine. The results create a new link between thermodynamics, information theory and complexity.

U2 - 10.1098/rspa.2012.0173

DO - 10.1098/rspa.2012.0173

M3 - Article (Academic Journal)

VL - 468

SP - 4058

EP - 4066

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2148

ER -