An educated review of

Abstract

The formulation of quantum work statistics as a dynamical problem through the Loschmidt echo is at the heart of this work. An introduction to each of these concepts is presented together with the notion of information scrambling, which extends the scope of this work to areas such as quantum chaos or even black hole physics. Using the paper of A. Chenu et al. [1] as the guidelines, we first show that the work statistics associated with an arbitrary driving protocol of an isolated quantum system in a generic initial state is equivalent to the Loschmidt echo dynamics of a purified density matrix in an enlarged Hilbert space. When the initial state is thermal, the purification leads to a thermofield double state, which is used to describe eternal black holes through the AdS/CFT correspondence, often argued to be the fastest information scramblers. The field of quantum chaotic systems is shown to emerge naturally from the previous content, and a full description of it in terms of Random Matrix Theory is also presented. Numerical and analytical results are finally obtained for the quantities introduced after imposing time-reversal symmetry in our problem, hence selecting the Gaussian Orthogonal Ensemble as the framework within we shall take our averages.