In contrast, if ρ ρ A ( T ) fails to approach a thermal density matrix even in the long time limit, and remains instead close to its initial condition ρ ρ A ( 0 ) , then the system retains forever a memory of its initial condition in local observables. This latter possibility is referred to as "many body localization," and involves B failing to act as a reservoir for A. A system in a many body localized phase exhibits MBL, and continues to exhibit MBL even when subject to arbitrary local perturbations. Eigenstates of systems exhibiting MBL do not obey the ETH, and generically follow an "area law" for entanglement entropy (i.e. the entanglement entropy scales with the surface area of subregion A). A brief list of properties differentiating thermalizing and MBL systems is provided below.