New Equilibrium Ensembles for Isolated Quantum Systems

Abstract

The unitary dynamics of isolated quantum systems does not allow a pure state to thermalize. Because of that, if an isolated quantum system equilibrates, it will do so to the predictions of the so-called "diagonal ensemble" ρ DE . Building on the intuition provided by Jaynes' maximum entropy principle, in this paper we present a novel technique to generate progressively better approximations to ρ DE . As an example, we write down a hierarchical set of ensembles which can be used to describe the equilibrium physics of small isolated quantum systems, going beyond the "thermal ansatz" of Gibbs ensembles.

Quantum coarse-grained entropy and thermalization in closed systems

“…Instead of defining entropy by instantaneous Hamiltonian, it is also possible to consider a more general case defined by any conceivable observable. The Shannon entropy of the diagonal elements of the density matrix written in an eigenbasis of an observable, which has been named "entropy of an observable" has been introduced in the 1960s [24,25] and studied recently [26][27][28]. This entropy is similar to what we study in this paper, however it does not take into account different sizes of the respective macrostates, and weights each of them the same, making it much less like the Boltzmann entropy; rather, it describes the statistics of measurement outcomes.…”