Roles of the Internal Coupling: From Equilibrium to Non-Equilibrium Dynamics

Abstract

We identify the precise thermodynamic roles of internal coupling in quantum thermal machines by analyzing the quantum Otto cycle across thermalized Gibbs-state limit cycles (GSLC) and finite-time non-equilibrating limit cycles (NELC). By systematically comparing the internally coupled system with standard and dressed-spectrum models, we resolve previous misconceptions regarding the physical origins of performance variations. First, we establish that the internally coupled system outperforms the standard system solely due to the Hamiltonian spectrum update, which intrinsically broadens the operating regimes. Second, we reveal that time-dependent efficiency and coefficient of performance (COP) are not caused by general quantum coherence, but specifically by eigenbasis mismatch arising from the non-commutativity of Hamiltonians across different strokes. The mismatch acts as quantum internal friction, reducing efficiency and COP and generating dissipative thermal modes. This results in the power-efficiency trade-off law, which we should find in realistic engines. However, we would not find the trade-off law when coherence exists but the eigenbasis mismatch does not exist, because there would be no friction, and hence the efficiency and COP would remain completely time-independent. Third, we isolate the distinct impact of coherence on power output. Validated by the global approach of the GKSL master equation, we demonstrate that coherence inherently reduces power by suppressing kinetic thermalization rates, regardless of eigenbasis mismatch.