Thermodynamics of Coherence-Selective Quantum Reset Protocols
We develop an exact theory of coherence-selective stroboscopic resetting for quadratic open quantum systems within the single-particle density-matrix formalism. We focus on the survival of coherences and the associated thermodynamic cost at the stroboscopic fixed point. To this end, we introduce a one-parameter family of reset channels that continuously interpolates between complete coherence erasure and complete coherence preservation. This unifies the reset-map description, the repeated-interaction and evolving-correlation endpoint channels, and the thermodynamic cost of environmental reinitialization. For a single fermionic level coupled to a structured semi-infinite tight-binding bath, we derive the exact affine stroboscopic map, solve for its unique fixed point, and compute the retained coherence spectrum, the post-reset occupation, and the reset heat current. We find that retained coherence increases monotonically with the retention parameter, whereas the reset heat current is generically nonmonotonic and is maximized at an intermediate operating point. Thus the protocol that stores the most coherence is not the one that dissipates the most heat. Exact operating diagrams further show that coherence-optimal and coherence-per-cost-optimal protocols are both driven toward the coherence-preserving endpoint, while the heat-optimal protocol depends strongly on the reset interval. We also show that this coherence-cost geometry survives at nonzero chemical potential as a filling-biased deformation of the same fixed-point tradeoff, rather than as an independent particle-current optimization problem. These results establish coherence-selective resetting as a distinct control principle for structured-bath open quantum systems and provide an exactly solvable benchmark for memory engineering and thermodynamic optimization under repeated environmental reinitialization.