Finite-Time Optimization of a Quantum Szilard Heat Engine

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 $\eta$ of QSE is bounded by $\eta \le 1 - (1-\eta_c \ln 2)/I(t_m)$ , where $I(t_M)/\ln 2$ 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 $P_O \propto t_m ^3$ in the short-time regime and as $P_O \propto t_m ^{-1}$ 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.

Physical Review Research