Finite-time optimization of a quantum Szilard heat engine

Abstract

We propose a finite-time quantum Szilard engine (QSE) with a spin-1/2 quantum particle as the working substance (WS) to accelerate the operation of information engines. We introduce a Maxwell's demon (MD) to probe the spin state within a finite measurement time t_{M} to capture the which-way information of the particle, quantified by the mutual information I(t_{M}) between WS and MD. We establish that the efficiency η of QSE is bounded by η≤1−(1−η_{C})ln2/I(t_{M}), where I(t_{M})/ln2 characterizes the ideality of quantum measurement, and approaches 1 for the Carnot efficiency reached under ideal measurement in quasistatic regime. We find that the output power of QSE scales as P_{O}∝t_{M}^{3} in the short-time regime and as P_{O}∝t_{M}^{−1} in the long-time regime. Additionally, considering the energy cost for erasing the MD's memory required by Landauer's principle, there exists a threshold time that guarantees QSE to output positive work.