Baron von Lotsov

It's entirely mathematical and based on probability theory. Molecules bump into each other and the chances of one being bumped in the same direction as the next one bumps it has an increasingly less of a chance of doing so and this is where you get your exponential fall off from. It is quantised energy as well but there will always be a small chance of some molecules reaching the escape velocity where they have more energy than their negative potential energy, by virtue of the fact they are bound to the earth in a gravitational field. It does not matter the size of the object and only that it is going faster than 11km/s and then it will keep going forever out into space. Some molecules have made it and we can calculate exactly what proportion do but it is likely to be very few indeed given that their average speed is only 500m/s.

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Besoeker

Thanks for that BVL.
I was aware of the general concept as you have succinctly described.
I covered (or was subjected to) all that. And the mathematics, of course.
My point about familiarity is that it is not a field I use in every day life.
Fourier series and Laplace transforms are mostly the tools I use these days.