Quantum Mechanical Models for the Szilard Engine

The Szilard engine combines concepts from thermodynamics, computation, and information theory to probe the validity of the second law of thermodynamics. By considering a single-molecule gas in a box with a movable partition, Szilard constructs a machine that extracts work from information at a single temperature. Quantum models have been proposed to generalize Szilard’s classical treatment to the quantum realm by considering a particle in a quantum box. Zurek¹ proposed a rigid box with a step barrier, and Davies² proposed a harmonic box with a delta function barrier. We probe the quantum model using an infinite rigid box with a delta function barrier. We slowly increase the strength of the barrier. We analyze the dependence of the solutions on the parameters of the box. We compute the thermodynamic quantities, including the entropy balance, throughout the Szilard cycle. We compare our results across the different box models. These results point us towards the development of quantum circuitry.

¹ W. H. Zurek, Physics Reports 755, 1 (2018)

² P. Davies, L. Thomas, and G. Zahariade, (2020), arXiv:2011.01180