Guaranteed Energy-Efficient Bit Reset in Finite Time

Landauer’s principle states that it costs at least $k_{B}T\ln 2$ of work to reset one bit in the presence of a heat bath at temperature $T$. The bound of $k_{B}T\ln 2$ is achieved in the unphysical infinite-time limit. Here we ask what is possible if one is restricted to finite-time protocols. We prove analytically that it is possible to reset a bit with a work cost close to $k_{B}T\ln 2$ in a finite time. We construct an explicit protocol that achieves this, which involves thermalizing and changing the system’s Hamiltonian so as to avoid quantum coherences. Using concepts and techniques pertaining to single-shot statistical mechanics, we furthermore prove that the heat dissipated is exponentially close to the minimal amount possible not just on average, but guaranteed with high confidence in every run. Moreover, we exploit the protocol to design a quantum heat engine that works near the Carnot efficiency in finite time.

Figure 1

“Bit reset” by raising ${\mathbf{E}}_{\mathbf{2}}$ to infinity. The numbers indicate the occupation probability for the energy levels. We consider the extension of this protocol, running in finite time.

Figure 2

A few steps of the protocol. Thermal (dashed line) and actual (solid line) upper energy level populations with respect to time. At each time $t(n)$ the upper energy level is raised, altering the thermal state.

Figure 3

Entropy-temperature diagram for the engine cycle. The block shaded area shows the net work exchanged by the system, which is less than that of the quasistatic (Carnot) cycle shown by the dashed rectangle filled with dots behind. For illustrative purposes, the number of energy level adjustments has been greatly reduced, and the size of the associated shifts in temperature greatly exaggerated.