Finite-Time Optimization of Quantum Szilard heat engine

TL;DR

This paper introduces a finite-time quantum Szilard engine utilizing a spin-based particle and Maxwell's demon, analyzing efficiency, power scaling, and energy costs to optimize quantum information engine performance.

Contribution

It develops a finite-time quantum Szilard engine model with a spin particle, deriving bounds on efficiency, power scaling laws, and conditions for positive work considering Landauer's principle.

Findings

Efficiency approaches Carnot limit under ideal measurement

Power scales as t_M^3 in short-time regime and t_M^{-1} in long-time regime

Existence of a threshold measurement time for positive work output

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 $t_{{\rm M}}$ to capture the which-way information of the particle, quantified by the mutual information $I(t_{\rm{M}})$ between WS and MD. We establish that the efficiency $\eta$ of QSE is bounded by $\eta\leq1-(1-\eta_{\rm{C}}){\rm ln}2/I(t_{{\rm M}})$, where $I(t_{{\rm M}})/\rm{ln}2$ 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 $P\propto t_{{\rm M}}^{3}$ in the short-time regime and as $P\propto t_{\rm M}^{-1}$ 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.