Figure 1

(a) Situation under investigation. The particle’s initial wave function ϕ 1 ( x ) (blue solid line) is the ground state which is confined between the tilted scaled potential V ˜ ( x ) = V ( x ) / ( ℏ / 2 m x 0 2 ) = x / x 0 (depicted as a solid red line) and the wall (in gray), initially located at the position x wall = 0 for the drawing. The generalized measurement is characterized by the function M o ( x ) (dotted line) able to tell that, for sure, the particle is outside the region [ x wall , x wall + ϵ x 0 ] when outcome o is found. (b) Energy exchanges occurring during the engine cycle: The measurement provides the quantum heat Q q , which is split between useful work W and the heat Q C dissipated in the cold bath. The dotted arrows stand for the details of the energy exchanges during the measurement according to our measurement model (see Supplemental Material [19]): The work W M is needed to entangle S and the meter, and E M is the average energy provided to the meter to reset it before the next cycle. (c),(d) Two possible implementations. (c) The elevator. An atom S is on a platform and experiences gravitational acceleration g . The detector D checks every cycle if the atom is within a distance ϵ from the platform and sends the outcome to the elevator operator O (lift attendant), who shifts the elevator to the “next floor” of height ϵ x 0 for free if the outcome is o . (d) The single-electron battery. The negatively charged particle experiences an electric field of intensity E between two electrodes. The wall is a piece of neutral insulator that can be moved depending on the outcomes of D . The electron successfully moved distance L between the electrodes charges the battery with energy e E L .