Leveraging Machine Learning to Gain Insights on Quantum Thermodynamic Entropy

We present a thermodynamic analysis of a quantum engine that uses a single quantum particle as its working fluid, inspired by Szilard's classical single-particle engine. Our design is modeled after the classically-chaotic Szilard Map and involves a thermodynamic cycle of measurement, thermal-energy extraction, and memory reset. Our focus is on investigating the thermodynamic costs associated with observing and controlling the particle and comparing these costs in the quantum and classical limits. Through our study, we aim to shed light on the thermodynamic trade-offs that arise from Lindauer's Principle for information-processing-induced thermodynamic dissipation in both the quantum and classical regimes. Using machine learning methods, we demonstrate that energy analysis can be performed and the quantum engine can be simulated according to the Szilard engine based Second Law of Thermodynamics in its working condition. However, we note that the quantum engine operates using significantly different mechanisms than its classical counterpart, where the cost of inserting partitions plays a critical role in the quantum implementation.