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Quantum Otto engine with a spin $1/2$ coupled to an arbitrary spin

We investigate a quantum heat engine with a working substance of two particles, one with a spin $1/2$ and the other with an arbitrary spin (spin $s$), coupled by Heisenberg exchange interaction, and subject to an external magnetic field. The engine operates in a quantum Otto cycle. Work harvested in the cycle and its efficiency are calculated using quantum thermodynamical definitions. It is found that the engine has higher efficiencies at higher spins and can harvest work at higher exchange interaction strengths. The role of exchange coupling and spin $s$ on the work output and the thermal efficiency is studied in detail. In addition, the engine operation is analyzed from the perspective of local work and efficiency. The local work definition is generalized for the global changes and the conditions when the global work can be equal or more than the sum of the local works are determined.