[IIAOPSW]

The imperfect mirror means that epsilon% of the time the light goes through to a much larger "back room" whereas (1-epsilon)% of the time the light just reflects like normal. The point being made is that this is an extension of an ordinary ideal cavity to include unavoidable (but weak) interaction with the much larger system outside of it (aka the whole universe). It just so happens the much larger external system is also being modeled as a simple 1d cavity.

In other words, entropy is equivalent to bits of information needed to specify the complete state of the system leaking outside of the confines of where those bits are being observed by an experiment (eg tunneling through an imperfect mirror).

Entropy is an accounting tool to keep track of how many bits are missing, and how far this ignorance has percolated into what you can safely predict about the system.