  The ecologist H. T. Odum introduced a principle of physics, called Maximum
Empower, in order to explain self-organization in a system (e.g. physical,
biological, social, economical, mathematical, ...). The concept of empower
relies on emergy, which is a second notion introduced by Odum for comparing
energy systems on the same basis. The roots of these notions trace back to the
50's (with the work of H. T. Odum and R. C. Pinkerton) and is becoming now an
important sustainability indicator in the ecologist community. In 2012, Le
Corre and Truffet developed a recursive method, based on max-plus algebra, to
compute emergy of a system. Recently, using this max-plus algebra approach, it
has been shown that the Maximum Empower Principle can be formalized as a new
combinatorial optimization problem (called the Maximum Empower Problem).
  In this paper we show that the Maximum Empower Problem can be solved by
finding a maximum weighted clique in a cograph, which leads to an
exponential-time algorithm in the worst-case. We also provide a polynomial-time
algorithm when there is no cycle in the graph modeling the system. Finally, we
prove that the Maximum Empower Problem is #P-hard in the general case, i.e. it
is as hard as computing the permanent of a matrix.
