Finite-Time Thermodynamic Routing in an Anharmonic Collective Quantum Otto Engine

The Gibbs state determined by a thermal reservoir does not determine how a working medium approaches it or how fluctuations accumulate over repeated cycles. We exploit this kinetic freedom in an anharmonic collective quantum Otto engine. A longitudinal interaction separates neighboring Dicke transition frequencies without changing their collective matrix elements, allowing passive spectral shaping to route finite-time transport among edges with different heat costs while preserving the contact Gibbs states. Exact edge-current identities and repeated-cycle counting statistics link this routing to mean work, hot heat, and intercycle work correlations. At fixed thermal-contact exposure, structured reservoirs can increase both mean work and long-time squared precision; equal-work controls distinguish these gains from uniform relaxation-rate changes. The useful regime is mesoscopic, bounded by spectral resolution and physical contact time. An equal-cooling example and a full-spin local-noise study test the mechanism beyond ideal engine operation, the latter retaining a one-cycle precision gain despite spin-sector mixing. In a six-transmon dressed-spectrum model, passive microwave filters at fixed integrated coupling achieve equal mean work with shorter thermal contacts, corresponding to higher contact-time-normalized output, and with long-time squared precision comparable to that of the fastest sampled flat reference. The transition pathways selected by a passive reservoir thus provide a control variable for finite-time performance and accumulated work fluctuations that is independent of thermal equilibrium.