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• Odum's Maximum Empower Principle is proved by using a correspondence between ecological theory and dynamic systems theory. • The empower computation is equivalent to a combinatorial optimization problem. • We introduce emergy state as a relevant set of flows of emergy for empower computation. • Emergy attractor is introduced as an emergy state which maximizes the empower. Self-organization is a process where order of a whole system arises out of local interactions between small components of a system. Emergy, spelled with an 'm', defined as the amount of (solar) energy used to make a product or service, is becoming an important ecological indicator. The Maximum Empower Principle (MEP) was proposed as the fourth law of thermodynamics by the ecologist Odum in the90′s to explain observed self-organization of energy driven systems. But this principle suffers a lack of mathematical formulation due to an insufficiency of details about the underlying computation of empower (i.e. emergy per time). For empower computation in steady-state an axiomatic basis has been developed recently by Le Corre and the second author of this paper. In this axiomatic basis emergy is defined as a recursive max-plus linear function. Using this axiomatic basis and a correspondence between ecological theory and dynamic systems theory, we prove the MEP. In particular, we show that the empower computation in steady-state is equivalent to a combinatorial optimization problem. [ABSTRACT FROM AUTHOR]