Finite-Time Optimization of Quantum Szilard heat engine

Abstract

We propose a finite-time quantum Szilard engine (QSE) with a quantum particle with spin 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 $t_{\mathrm{M}}$ to capture the which-way information of the particle, quantified by the mutual information $I(t_{\mathrm{M}})$ between WS and MD. We establish that the efficiency $\eta$ of QSE is bounded by $\eta \le 1-(1-{\eta }_{\mathrm{C}})\ln 2/I(t_{\mathrm{M}})$, where $I(t_{\mathrm{M}})/\ln 2$ characterizes the ideality of quantum measurement, and approaches $1$ for the Carnot efficiency reached under ideal measurement in quasi-static regime. We find that the power of QSE scales as $P\propto t_{\mathrm{M}}^3$ in the short-time regime and as $P\propto t_{\mathrm{M}}^{-1}$ 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.

arXiv comment6+10 pages, 3+4 figures, Comments are welcome

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