Accuracy of energy measurement and reversible operation of a microcanonical Szilard engine

Abstract

In a recent paper [Vaikuntanathan and Jarzynski, Phys. Rev. E {\bf 83}, 061120 (2011), arXiv:1105.1744] a model was introduced whereby work could be extracted from a thermal bath by measuring the energy of a particle that was thermalized by the bath and manipulating the potential of the particle in the appropriate way, depending on the measurement outcome. If the extracted work is $W_1$ and the work $W_{\text{er}}$ needed to be dissipated in order to erase the measured information in accordance with Landauer's principle, it was shown that $W_1\leq W_{\text{er}}$ in accordance with the second law of thermodynamics. Here we extend this work in two directions: First, we discuss how accurately the energy should be measured. By increasing the accuracy one can extract more work, but at the same time one obtains more information that has to be deleted. We discuss what are the appropriate ways of optimizing the balance between the two and find optimal solutions. Second, whenever $W_1$ is strictly less than $W_{\text{er}}$ it means that an irreversible step has been performed. We identify the irreversible step and propose a protocol that will achieve the same transition in a reversible way, increasing $W_1$ so that $W_1 = W_{\text{er}}$.