Dynamics of Information Quantifiers in the Damped Rabi Oscillator

This study examines the time evolution of structural and informational quantifiers in a damped Rabi oscillator, specifically focusing on fidelity, entropy, disequilibrium, and Fisher information. We observe that all four measures exhibit damped oscillatory behavior as the system approaches its steady state. However, the final asymptotic behavior is striking: while fidelity and disequilibrium indicate a residual, non-zero final state, and entropy quantifies the thermodynamic disorder, Fisher information uniquely vanishes. This vanishing implies a complete loss of dynamical information—the ability to infer the system's past evolution from its current state—even in the absence of complete thermodynamic disorder. Our findings introduce a new phenomenon where a system can be "informationally silent," meaning it becomes structurally ordered yet loses all inferential sensitivity to its own history, a detail that traditional entropy measures do not fully capture. This work highlights a critical distinction between thermodynamic disorder (entropy) and inferential sensitivity (Fisher information) in the context of open quantum systems.