  We discuss a model of a closed quantum evolution of two-qubits where the
joint Hamiltonian is so chosen that one of the qubits acts as a bath and
thermalize the other qubit which is acting as the system. The corresponding
exact master equation for the system is derived. Interestingly, for a specific
choice of parameters the master equation takes the
Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form with constant coefficients,
representing pumping and damping of a single qubit system. Based on this model
we construct an Otto cycle connected to a single qubit bath and study its
thermodynamic properties. Our analysis goes beyond the conventional weak
coupling scenario and illustrates the effects of finite bath including
non-Markovianity. We find closed form expressions for efficiency (coefficient
of performance), power (cooling power) for heat engine regime (refrigerator
regime) for different modifications of the joint Hamiltonian.
