Critical Crossings and Quantum Friction in a Finite-Time $XY$-Chain Otto Engine

Abstract We investigate the finite-time performance of a quantum Otto engine with a transverse-field anisotropic $XY$ spin chain as its working medium. By decomposing the chain into independent momentum sectors, we calculate mode-resolved transition probabilities during linear transverse-field ramps. We determine the resulting excitation density, work, heat, efficiency, and power for driving protocols in which the transverse field is varied linearly between prescribed endpoints during the two unitary strokes, while the anisotropy remains fixed. Protocols crossing one or both quantum critical points exhibit Kibble--Zurek scaling, $n_{\mathrm{ex}}\sim\tau^{-1/2}$, whereas protocols that maintain a nonzero energy gap throughout the ramps exhibit the faster decay $n_{\mathrm{ex}}\sim\tau^{-2}$, where $\tau$ is the duration of each ramp. The work separates into an endpoint-dependent adiabatic contribution and a nonnegative contribution associated with quantum friction. At short driving times, quantum friction can exceed the adiabatic work output and prevent heat-engine operation. At long driving times, the thermodynamic quantities approach adiabatic values determined by the endpoint spectra and thermal population imbalances. Increasing anisotropy suppresses excitations and hastens the approach to the adiabatic limit. These results distinguish endpoint thermodynamics from critical-crossing dynamics and clarify their roles in finite-time engine performance.