Codification volume of an operator algebra and its irreversible growth through thermal processes

Abstract

Given a many-body system, we define a quantity, the codification volume of an operator algebra, which measures the size of the subfactor of the full Hilbert space with which a given algebra is correlated. We explicitly calculate it for some limit cases, including vacuum states of local Hamiltonians and random states taken from the Haar ensemble. We argue that this volume should grow irreversibly in a thermalization process, and we illustrate it numerically on a nonintegrable quantum spin chain.