The Funessian process: Non-Markovian dynamics shaped by the first event (opens in new tab)

We construct a continuous-time, positively divisible non-Markovian process with memory of the initial state that satisfies the differential Chapman--Kolmogorov equation. In the stationary state, the correlation function exhibits exponential decay, a behavior typically regarded as characteristic of Markovian dynamics. Nevertheless, the memory is preserved throughout the evolution of the process, manifesting itself in observable statistical quan...