Sustainability assessment is an important subject in the field of sustainable development. Indicators of sustainability can provide policy-makers with clues as to whether a region is moving toward or away from sustainability: this can be helpful for decision-making. Sustainability assessment methodologies can be classified into three indicators: enumeration, flow analysis and systemic analysis. The standard used to classify methodologies considers whether the relationships between components in the system alone or whether the relationships between components in the system and the outside environment are considered. The indicators enumeration and flow analysis are widely used; however, they contain some disadvantages. These methods have a poor theoretical basis. Moreover, criteria to choose, standardize and integrate indicators are not ascertained unanimously. Different results may be derived for the same data if different methods of standardization or integration are used. Hence, sustainability assessment from the perspective of system dynamics has emerged as the optimal assessment method. In 2009, the American theoretical ecologist Ulanowicz proposed a typical system analysis method known as the evolution model. The evolution model-taking flow networks as the study object vand information theory as the measurement-shows that the sustainability of a system is determined by the balance between ascendency (efficiency) and resiliency. The model states that the capacity for a system to undergo evolutionary change or self-organization consists of two factors: 1) ascendency: the network's capacity to perform in a sufficiently organized and efficient manner to maintain its integrity over time; and 2) resilience: the network's reserve of flexible fallback positions and diversity of actions that can be used to meet the exigencies of novel disturbances and the novelty needed for ongoing development and evolution. These two factors are complementary with respect to diversity and connectivity in the network. A system's resilience is enhanced by high levels of diversity and connectivity, while ascendency is augmented by low levels of diversity and connectivity. In other words, too much ascendency (resilience) means too little resilience (ascendency). A system lacking ascendency has neither the extent of activity nor the internal organization needed to survive. By contrast, a system lacking resilience appears brittle in the face of novel disturbances. Both too much ascendency and too much resilience negatively affect sustainable development. Both ascendency and resilience are important for long-term sustainability: a system's sustainability is depending on the tradeoff between ascendency and resilience. According to this result, the sustainability indicator R is proposed. The paper is organized as follows. First, the advantages and disadvantages of current sustainability assessment methodologies are reviewed. Section 1 describes the principles used to analyze sustainability from the perspective of system's evolution. In section 2, the evolution model is described in the language of information theory. Section 3 describes the range of sustainable development and the optimal sustainable development state for ecosystems. This section also examines how to analyze the range of sustainable development in an economic system. The evolution model is applied to a water system and an economic system; these applications are described in section 4. Finally, the key steps to applying the evolution model are summarized and its disadvantages are discussed.