We review recent progress on the information paradox. We explain why exponentially small
correlations in the radiation emitted by a black hole are sufficient to resolve the original …

This review gives a pedagogical introduction to the eigenstate thermalization hypothesis
(ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first …

The thermodynamic description of many-particle systems rests on the assumption of
ergodicity, the ability of a system to explore all allowed configurations in the phase space …

A bstract Inspired by the universal operator growth hypothesis, we extend the formalism of
Krylov construction in dissipative open quantum systems connected to a Markovian bath …

The entanglement entropy of subsystems of typical eigenstates of quantum many-body
Hamiltonians has recently been conjectured to be a diagnostic of quantum chaos and …

Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an
unprecedented perspective for solving intricate quantum many-body problems …

We develop a theory of symmetry in open quantum systems. Using the operator-state
map**, we characterize symmetry of Liouvillian superoperators for the open quantum …

We review selected advances in the theoretical understanding of complex quantum many-
body systems with regard to emergent notions of quantum statistical mechanics. We cover …

We show that out-of-time-order correlators (OTOCs) constitute a probe for local-operator
entanglement (LOE). There is strong evidence that a volumetric growth of LOE is a faithful …

A bstract Quantum complexity, suitably defined, has been suggested as an important probe
of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of …