Thermodynamics of complexity measures
Physical systems are often simulated using a stochastic computation where different final states result from identical initial states. Here, I derive the minimum energy cost of simulating a data sequence of a general physical system by stochastic computation. Using information theory, I 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. I derive the difference as the amount of information erased during the computation. To this framework I will add a quantum mechanical measure of complexity. The resulting triple opens an interesting view on thermodynamics, quantum mechanics and complexity.