Cross-Spectral Reservoir Correlations as a Resource for Finite-Time Quantum Otto Engines
We investigate the thermodynamic consequences of longitudinal-transverse cross-spectral reservoir correlations in a finite-time quantum Otto engine with a two-level working medium. Each reservoir couples through excitation-relaxation and dephasing channels whose fluctuations are characterized by a Hermitian positive-semidefinite spectral-density matrix, with the off-diagonal elements encoding their cross correlations. The finite-time isochoric dynamics is derived within the second-order time-convolutionless framework, without imposing the Markov limit at the outset, so that finite reservoir-memory effects can enter through time-dependent dissipative and reservoir-induced coherent contributions. The resulting dynamics is then recast in Bloch-vector form to construct the stroke-resolved cycle dynamics. At fixed auto-spectral densities, cross-spectral correlations modify the populations and coherences of the working medium and thereby its thermodynamic performance. Increasing the correlation strength can enhance the output power, with the enhancement controlled by the cross-spectral phase and characteristic frequency scale. The correlations also reshape the transient cycle-to-cycle evolution and the approach to periodic operation, while the limit-cycle efficiency remains fixed at the Otto value for the population-preserving unitary strokes considered here. These results establish off-diagonal reservoir spectra as an additional resource for controlling finite-time quantum thermal machines.