Entropy production in quantum systems and Nernst heat theorem for a single qubit

Abstract

Classical thermodynamics, which focuses on macroscopic systems in equilibrium, has given rise to various theories to address systems out of equilibrium over time. Recently, quantum thermodynamics has emerged as a theory dedicated to describe microscopic quantum systems. A notable application of this theory is found in the development of thermal engines, where the working substance is a microscopic quantum system. In this work, we present the essential theoretical formulation to understand entropy production in quantum systems and its impact on thermal machines. The approach involves exploring quantum friction and conducting a deeper analysis of the laws of thermodynamics on a fundamental scale. Examining the effects of these phenomena in a Quantum Otto Heat Engine, we highlight the implications of quantum friction on engine performance. Particularly noteworthy is the observation that operating the cycle with a reservoir with effective negative temperature enhances the engine efficiency significantly. This improvement is attributed to strategic choices in the populations of excited states in the reservoirs, revealing an innovative approach to optimizing performance in quantum systems. Additionally, we extend the Nernst heat theorem for a single qubit. This result not only presents intriguing theoretical implications but is also supported by numerical simulations and experiments using Nuclear Magnetic Resonance (NMR). These pieces of evidence uphold the remarkable convergence of Helmholtz free energy and internal energy as the temperature approaches zero Kelvin, underscoring the practical applicability of these theorems in quantum systems.