Quantum thermodynamic resources and bounds on the performance of quantum otto engines

Abstract

Quantum thermodynamics is an emerging research field aiming to close the newlinegap between the microscopic world of quantum mechanics and the macro- newlinescopic world of classical thermodynamics by establishing a novel thermo- newlinedynamic framework that incorporates and exploits non-classical resources newlineof quantum discreteness, correlations, entanglement and so on. To achieve newlinethis goal, quantum analogues of classical heat engines serve as test beds to newlinedemonstrate extensions of thermodynamic ideas into the quantum realm. newlineMultifarious proposals for quantum heat engines or refrigerators have been newlineproposed. Amongst these, the study of simple, coupled quantum systems newlineyield important insights into the role of quantum interactions in enhancing newlinethe performance of model thermal machines. One of the major issues be- newlineing addressed in these models is: What are the thermodynamic constraints newlineand bounds on the performance of these quantum thermal machines? newlineIn the present work, quantum Otto engines (QOEs), with quantum spins newlineas the working substance, have been investigated. An Otto cycle is widely newlinestudied in literature, because the contributions of heat and work can be newlineclearly separated into different steps during the heat cycle. We begin by newlineconsidering two coupled, effectively two-level systems each with a degen- newlineerate excited state, and then generalize it to the case of two coupled spins of arbitrary magnitudes. For a quasi-static QOE, we prove that level de-generacy can act as a thermodynamic resource, helping to extract a larger newlineamount of work than in the non-degenerate case, either without coupling or newlinein the presence of coupling. We compare our analysis with earlier studies on newlinethe role of level degeneracy in finite-time models of thermal machines. Fur- newlinether, by carefully making use of the information from the energy spectrum newlineof the working medium, we look for conditions to better the performance of the coupled system over its uncoupled counterpart using heuristics based approach. An upper bound for the efficiency of the Otto cycle has thu