We introduce a generalized comb geometry based on a continuous-time random walk that unifies longitudinal advection, transverse trapping, and reversible reactions with temporal memory. By deriving macroscopic evolution equations from this microscopic stochastic process, we establish a direct link between waiting-time statistics and three distinct memory functions. Our framework reveals that temporal memory in longitudinal motion drives long-time superdiffusion, whereas memory in transverse exploration leads to subdiffusion. Furthermore, reaction memory governs the exchange between free and reactive populations, leading to algebraic growth of spatial non-Gaussianity in irreversible regimes and a constant non-Gaussian signature in the transverse direction. We find that ergodicity breaking is determined by the slower of two relaxation processes: branch exploration or reaction unbinding. This work bridges single-particle tracking with continuum modeling, uncovering the competition and synergy among distinct memory mechanisms to provide exact analytical benchmarks for reactive transport in disordered media.

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• Nonequilibrium statistical mechanics
• Random walks
• Thermodynamics