What kind of physical processes are well modeled as poisson processes? For instance, it is easy to understand how Brownian motions appear: when an object receives many small shocks that are roughly i.i.d., the resulting path will look like Brownian motions.
What type of physical processes give rise to Poisson processes?
For instance, with one dimension thought of as time: what kind of physically processes would naturally have the "memoryless property" between spikes?

Consider yourself driving a car in the rain and counting how many rain drops fall on your windscreen per second. None of these raindrops has any memory whatsoever of how many of the other raindrops reached your windscreen.
$\lambda$ will depend on your driving speed.
