Physics does not emphasize this, but the half life concept essentially assumes a Poisson process (Cinlar, Stochastic Processes) which has a Markov (past and future conditionally independent given the present, details from the Radon-Nikodym theorem, with a cute von Neumann polynomial proof, Rudin, Real and Complex Analysis) assumption.

The half life concept seems to be standard over much of physics.

That a Markov assumption could hold might suggest some new physics.