  Quantum thermodynamics with microscopic inelastic scattering processes has
been intensively investigated in recent years. Here, we apply quantum master
equation combined with full counting statistics approach to investigate the
role of quantum coherence on the periodically-driven inelastic heat engine. We
demonstrate that the inelastic quantum heat engine exhibits dramatic advantage
of thermodynamic performance compared to their elastic counterpart. Moreover,
it is found that inelastic currents, {output work}, and the efficiency can be
enhanced by quantum coherence. In particular, the geometric effect proves
crucial in achieving maximal values of generated output work and energy
conversion efficiency. The Berry curvature boosted by quantum coherence unveils
the underlying mechanism of periodically-driven inelastic heat engine. Our
findings may provide some insights for further understanding and optimizing
periodically-driven heat engines via quantum coherence resource and inelastic
scattering processes.
