I've been discussing in some detail here a mathematical model of the response of Earth's climate to radiative forcings, trying to address some of the concerns expressed elsewhere on the need for such a model to be "physically realistic". In the case of the two-box model, a given fit of the response function to a two-time-constant decay curve could come from one of many different underlying physical models that correspond to a partitioning of Earth's climate system into two parts with different response rates. So the question has been whether any of these possible underlying physical models are in some way "realistic" or not. That essentially reduces to criteria on the magnitude of the various constants and partial outcomes in the model relative to real components of our planet.