Fig. 2: Pure-state qubit trajectories for the work extraction protocol.
From: Energetic footprints of irreversibility in the quantum regime
Illustration of the evolution of the qubit during the work protocol on the trajectory level and on the density matrix level. The qubit’s trajectories are deterministic during Steps (I) (unitary, green arrows), (II) (quench, black arrows), and (V) (quench, black arrows), i.e., they take one state to a unique other state. In contrast, during the decoherence part in Step (III) (blue dashed arrows) the qubit stochastically jumps from one of the states \(|{\tilde{\theta}}_{\pm}\rangle\) to one of the energy eigenstates \(\left|{e}_{\pm }\right\rangle\), thus losing any quantum coherence in an irreversible manner. During the classical thermalization part in Step (III) (red arrows) the qubit stochastically jumps from one of the energy eigenstates to another energy eigenstate, thus losing any classical non-thermality in an irreversible manner. The qubit’s trajectories during the classical quasi-static isothermal change of H (Step (IV), orange arrows), are stochastic but reversible, due to infinitely small thermalizations taking place throughout.
