Anomalous diffusion is well studied in complex environments where viscoelasticity, crowding, and nonequilibrium activity strongly influence particle motion. Several biological systems are not independent; rather, they are coupled to another system, which shows distinct viscoelastic responses and heterogeneous transport behavior. We have developed a theoretical model of an active and a passive particle, coupled via a harmonic interaction, whose motion is restricted to a plane within a viscoelastic medium described by a generalized Langevin framework with a long-tailed power-law memory kernel. We obtained analytical expressions for the mean-squared displacement (MSD) and interparticle separation. We demonstrate that the coupled system shows multiple dynamical crossovers such as subdiffusive, ballistic, and diffusive transport regimes, whose emergence is controlled by the relative viscoelastic exponents and coupling strength. Specifically, we show that long-term dynamics is mainly controlled by the subdiffusive component, where the passive particle can suppress activity and the active particle can dominate and drive enhanced transport. Our results also highlight non-Gaussian displacement statistics at intermediate lag times. These findings provide insight into coupled transport in active matter systems, including tethered biomolecules, molecular motors, cytoskeletal networks, and synthetic microswimmers in complex media.

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• Langevin equation
• Markovian processes
• Non-Markovian processes
• Phase space dynamics
• Stochastic analysis