Study of bounds on non-equilibrium fluctuations for asymmetrically driven quantum otto engine

For a four stroke asymmetrically driven quantum Otto engine with working medium modeled by a single qubit, we study the bounds on non-equilibrium fluctuations for work and heat. We find strict relations between the fluctuations of work and individual heat for hot and cold reservoirs in arbitrary operational regime. Focusing on the engine regime, we show that the ratio of non-equilibrium fluctuations for output work and input heat from the hot reservoir is both upper and lower bounded. As a consequence, we establish interesting hierarchical relation between the relative fluctuations of work and heat for both cold and hot reservoirs and further make a connection with the thermodynamic uncertainty relation. We discuss the fate of these bounds also in the refrigerator regime. The reported bounds, for such asymmetrically driven engines, emerge once both the time-forward and the corresponding reversed cycles of the engine are considered on an equal footing. We also extend our study and report bounds for a parametrically driven harmonic oscillator Otto engine.