First passage properties of evanescent run-and-tumble particles

Evanescent run-and-tumble particles are self-propelled agents that may disappear due to decay, degradation, or other removal mechanisms. In this work, we study their first-passage behavior in one spatial dimension within a finite domain bounded by a reflecting and an absorbing boundary wall. Using a Laplace-space generating-function framework, we derive closed analytical expressions for the eventual absorption probability and the conditional mean first-passage time (CMFPT) in the case of uniform mortality. We show that mortality fundamentally changes first-passage statistics. The eventual absorption probability becomes less than one, and the conditional mean first-passage time decreases monotonically as the death rate increases, reflecting the suppression of long ballistic trajectories. Monte Carlo simulations are in excellent quantitative agreement with the analytical predictions across all parameter values considered. We also outline a general analytical framework for position-dependent death rates. Together, these results provide a consistent theoretical description of first-passage processes in mortal active systems and clarify how evanescence shapes survival and absorption dynamics.