2.1.2. Energy Flows—Cascading

Energy can be sourced either from renewable sources (mainly of solar origin) or from terrestrial deposits (Figure 4). Energy flows follow the Laws of Thermodynamics, cascading from higher to lower quality [69]. Harvested energy flows can be used to power various processes, resulting in the movement of the material flows within a system; i.e., an enterprise, a municipality, or a region. At the system level, at various scales, energy can be sourced, converted and used and ultimately is left to dissipate in the environment. The share of the losses to dissipation reaches two-thirds [70]. This pattern reveals that there are two types of global system interface flows: energy inlets (renewable) and energy outlets (dissipation). Any non-renewable energy sources are internal to the system. This allows the classification of renewable energy sources as long-term degrees of freedom and the non-renewable as short term ones.

Energy cascading is thus used to power the closed material cycles for industrial and other activities in the global economy. Establishing this principle allows us to set up a framework for system state accounting which can be used to evaluate and optimise the system design and operation for various objective functions linked to the energy supply.

**Figure 4.** Energy cascading; data extracted from [70]. PV: photovoltaics.

The analysis in this section clearly points to energy harvesting and use as the dominating factor, representing a key degree of freedom in driving the economy and societal activities. Moreover, energy is stored in various forms for conversion, transport and use. This view of energy transformations allows the consideration of industrial and business processes as networks of states and transitions, where the states are related to the energy content of materials and process streams, while the transitions are either intentional process operations or spontaneous transitions, transforming process streams from one state to another at the expense of exergy conversion and destruction.

There have been many proposed circular economy indicators; e.g., a recent review [59] analysed 55 sets of circularity indicators. The choice and most beneficial use of indicators depends on the considered context. Within the context of a given supply chain or an industrial process, the degree of recycling of key materials is the most widely used indicator; in this context, the Circular Material Use rate (CMU) has been adopted by Eurostat [71] to determine the degree of circularity of systems at various scales. In the case of Eurostat, this is applied to measure the circularity of the economies of EU member states. CMU is defined, within the context of a specific material, as the fraction of the recycled material (U) within the overall material intake by the system (M):

$$\text{CMU} = \frac{\text{U}}{\text{M}} \tag{1}$$

While CMU is a crucial indicator, it alone is not sufficient to characterise the sustainability of the considered systems. Additional indicators are therefore needed to provide sufficient characterisation. The model proposed here uses energy as the main indicator, in the form of exergy, with all remaining system properties used as specifications to ensure the sustainable conditions of all parts of the environment–economy–society macro-system.
