Escape-rate formalism, decay to steady states, and divergences in the entropy-production rate

In summer 1997 we were sitting with Bob Dorfman and a few other friends interested in chaotic systems and transport theory on a terrace close to Oktogon in Budapest. While taking our (decaf) coffee after a very nice Italian meal, we discussed about logarithmic divergences in the entropy production of systems with absorbing boundary conditions and their consequences for the escape-rate formalism. It was guessed at that time that the problem could be resolved by a careful discussion of the physical content of the absorbing boundary conditions. To our knowledge a thorough analysis of this long-standing question is still missing. We dedicate it hereby to Bob on occasion of his 65th birthday.