In comments to a Phys.SE question, it has been written:
'Tunneling' is perfectly real, even in classical physics. […] For sufficiently large temperatures this can put the system above a hump in its potential energy.
and
the only difference between the classical case and the quantum mechanical one is that classical physics is a random walk in real time, while QM is a random walk in imaginary time.
I understand that in a system of particles with finite temperature some particles can overcome a potential barrier. That's how I interpret the first statement. I don't understand the business of "random walk in imaginary time". Can someone explain?
Update
What I was originally looking for was 1.) classical system that can transport mass through a forbidden region and 2.) explanation of "random walk in imaginary time". So far, I don't see anything for question 1.), but I think I'll grok 2.) if I invest some time and energy.
Best Answer
Frustrated total internal reflection is an optical phenomenon. It's such a close analogue to quantum tunneling that I sometimes even explain it to people as "quantum tunneling for photons". But you can calculate everything about it using classical Maxwell's equations.