Construction of a quantum Carnot refrigerator for general working substances

A general framework is proposed for constructing a six-stroke irreversible Carnot refrigerator with a working medium characterized by discrete, non-scalable energy levels. A working substance-dependent correction to the coefficient of performance (COP) is expressed in terms of a positive lag term, establishing the ideal Carnot COP as the upper bound for general working media. Three distinct design scenarios for the Carnot refrigerator cycle are presented. Two dipole-coupled spins in a tunable field are employed as the working substance. A comparison of work input, cooling heat, and COP is conducted for the coupled working medium under three design scenarios. The study highlights qualitative differences between the approaches, particularly in the coupled spin case, providing valuable insights into the performance and limitations of refrigeration cycles under varying operational constraints.