Quantum thermal machines in BTZ black hole spacetime

We investigate an Otto thermodynamic cycle with a qubit Unruh-DeWitt detector as the working medium, coupled to a massless, conformally coupled scalar quantum field in the Hartle-Hawking vacuum in a (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math>)-dimensional BTZ black hole spacetime. We employ the thermal properties of the field to model heat and cold reservoirs between which the thermal machine operates. Treating the detector as an open quantum system, we employ a master equation to study its finite-time dynamics during each cycle stroke. We evaluate the output performance of the Otto heat engine and refrigerator by computing, respectively, the total work output and the cooling power for each of the Neumann, transparent, and Dirichlet boundary condition cases satisfied by the field at spatial infinity. Furthermore, we evaluate the optimal performance of the thermal machine by analyzing its efficiency at maximum power output and ecological impact. Our study presents a general framework for understanding the finite-time operation of relativistic quantum thermal machines, focusing on their energy optimization.