Non-commutative space engine: a boost to thermodynamic processes

We introduce quantum heat engines that perform quantum Otto cycle and the quantum Stirling cycle by using a coupled pair of harmonic oscillator as its working substance. In the quantum regime, different working medium is considered for the analysis of the engine models to boost the efficiency of the cycles. In this work, we present Otto and Stirling cycle in the quantum realm where the phase space is non-commutative in nature. By using the notion of quantum thermodynamics, we develop the thermodynamic variables in non-commutative phase space. We encounter a catalytic effect (boost) on the efficiency of the engine in non-commutative space (i.e. we encounter that the Stirling cycle reaches near to the efficiency of the ideal cycle) when compared with the commutative space. Moreover, we obtained a notion that the working medium is much more effective for the analysis of the Stirling cycle than that of the Otto cycle.