  The collapse of large social systems, often referred to as civilizations or
empires, is a well known historical phenomenon, but its origins are the object
of an unresolved debate. In this paper, we present a simple biophysical model
which we link to the concept that societies collapse because of the diminishing
returns of complexity proposed by Joseph Tainter. Our model is based on the
description of a socioeconomic system as a trophic chain of energy stocks which
dissipate the energy potential of the available resources. The model produces
various trajectories of decline, in some cases rapid enough that they can be
defined as collapses. At the same time, we observe that the exploitation of the
resource stock (production) has a strongly nonlinear relationship with the
complexity of the system, assumed to be proportional to the size of the stock
termed bureaucracy. These results provide support for Tainter s hypothesis.
