Abstract
The understanding of the emergence of equilibrium statistical mechanics has progressed significantly thanks to developments from typicality, canonical and dynamical, and from the eigenstate thermalization hypothesis. In this dissertation, we focus on the nonequilibrium (quasi)-steady states in two different scenarios. The first scenario applies systems that follows eigenstate thermalization hypothesis where we study the applicability of treating these systems as interacting environments. In particular, we address the concept of typicality for nonequilibrium quasi-steady current by exploiting pure initial states from these environments. Different types of initial states including the eigenstate, random superpositions of eigenstates, and random product states from the mean energy ensemble are discussed. We also identify that currents formation follows the prethermalization mechanism, which is the weak breaking of the conservation of the energy for each environment. Last, we show that the coupled environments eventually thermalize with a universal timescale set by the environment’s size and their coupling strength. The second scenario focuses on the antithesis of eigenstate thermalization, i.e., many-body localized systems which fail to thermalize. We first revisit the notion of localization for steady states and study the signatures of localization in the steady state for such many-body localized systems under tailored dissipations. We study the effects of a particular type of environment which tries to drive the system towards a highly delocalized state, while the presence of disorder, together with the interaction between the particles, could result in a localized system.