Information and entropy in the baker’s map

Abstract

We analyze a random perturbation applied to the baker’s map, a prototype for chaotic Hamiltonian evolution. We compare two strategies for following the perturbed evolution: (i) tracking the perturbed pattern in fine-grained detail; (ii) coarse graining by averaging over the perturbation. We find that the Landauer erasure cost associated wtih the information needed to implement the first strategy is overwhelmingly larger than the standard free-energy reduction associated with the second strategy. This finding provides a quantitative justification for coarse graining and thus an explanation of the second law of thermodynamics.