Non-equilibrium thermodynamics of quantum processes assisted by transitionless quantum driving: the role of initial state preparation

Abstract: Adiabatic evolution is considered to be the ideal situation for most thermodynamic cycles, as it allows for the achievement of maximum efficiency. However, no power output is produced in light of the infinite amount of time required to perform a transformation. Such issue can be overcome through Shortcuts-To-Adiabaticity (STA) protocols, which allows a dynamics to mimic its adiabatic counterpart, but in a finite time. Transitionless quantum driving (TQD) is one form of STA. We develop and study the effects of TQD on a single-qubit system subjected to a changing magnetic field and a general two-qubit Heisenberg model with a time-dependent interaction strength. We establish a quantitative relation between the work produced across the dynamics and the entropy production resulting from the evolution at hand, focusing on the role played by the initial states of the work medium. We identify the states that extremize performance under the TQD protocol. The thermodynamic implications of STA are discussed in the end.