## The Ratio of A Ex to AEm

From the reasoning above it is also possible to investigate another problem: how does an ecosystem respond if there is a change in inputs with regard to its self-organization.?

This problem can be seen in emergy flows and eco-exergy terms. Let us consider the emergy flow to a system to vary between two equal and contiguous intervals (these intervals must be significant for the system under study in order to annul the effect of periodical variations like daily and seasonal cycles). We indicate the variation of emergy flow with AEm. Now the question is 'what will be the change in organization due to the change in emergy input AEm?' To answer this question we have to be able to calculate the variation of the eco-exergy content of the system AEx. We can therefore examine the quantity

_ AEx a ~ AEm with the dimensions ofJssej-1, and represent the change of level of organization (eco-exergy) of the system under study, when it is involved in a change of the emergy flow. It is a quantity that is specific to the inputs that are subtracted or added.

A two-dimensional diagram can be used to explain what scenarios are possible (Figure 2): if a is positive, the addition of emergy input gives rise to further organization, whereas a lowering of emergy has a negative effect on the system. On the other hand, when a is negative, a higher emergy flow causes a decrease in organization or a lower quantity of one or more inputs causes increasing organization. We can say that in both the latter cases the inputs (added or removed) can generally be regarded as pollutants: if we remove them, the system self-organizes; if we add them, the system is damaged. So we can have a definition of pollution based on two orientors, emergy flow and eco-exergy, that focus their attention not on particular aspects of a system, but on the system as a whole. The intensity of the 'pollution' is proportional to the absolute value of the slope of the segment connecting the origin to the point that describes the system, since a small increase (decrease) in emergy flow produces a large loss (gain) of

AEx a

Figure 2 Two-dimensional diagram of the relationship between the change of emergy flow (AEm) and the change of exergy (AEx).

organization. The same reasoning can be applied to the cases where a is positive. The slope of the line connecting the point with the origin represents the benefit that a set of inputs - when added - is able to produce on a system.

The points on the diagram correspond to singular situations that can evolve over time. We have a succession of points, one for each subsequent interval, during which we can calculate the emergy flow. To clarify this point we refer to what we previously said about the differences existing between emergy and eco-exergy also from a mathematical viewpoint. Let us consider t0, t1, ..., tk _ b tk, tk +1,... a set of points at the axis of time, representing the extrema of the closed intervals on which we calculate the emergy flows to the system, Em([t0, t1]),..., Em([tk _ 1, tk]), Em([tk, tk +1]), In correspondence of each point t, we can also calculate the eco-exergy Ex(,). The succession of points of the ratio AEx/AEm can be written as

_ Ex(tk+i) - Ex(tt) Em([tk, tk+i ]) - Em ([tk - u tk\)

where ak is the ratio calculated considering the differences between the two flows of emergy during the intervals [tk, tk +1] and [tk_ 1, tk], and the value of the eco-exergy at the right extrema of these two intervals. In this way we have a succession of ak points which represent the way the system responds to changing surrounding conditions. We can consider a succession starting from a point 6 with a negative value of a to a point with a positive value of a. These would mean that the system is 'learning' how to use other available inputs and the system self-organizes. On the other hand, a pattern of inputs that is initially positive for a system can become negative if there is a longer-term toxic effect. As an example of the application of this concepts consider the change in the composition of rain that falls upon a forest. If the rain becomes more acidic, its emergy content rises as does the emergy flow through the forest. On the other hand, the eco-exergy of the forest is likely to decrease because of the loss of biomass density and of the consequent loss of biodiversity. In this case a would be negative at least until the acidity of the rain decreases again or the species in the forest learn how to survive in the modified environment or how to use a different input. This framework has been found helpful in solving some shortcomings of the use of a pure life cycle assessment (LCA) approach; in LCA, there is a lack of systematic and quantitative framework that does not allow comparison of the environmental sustainability of processes, when we want to consider both the use of resources and the global effects of the outputs of a process. The use of emergy and eco-exergy, and especially a wider use of the ratio of the variations of eco-exergy and empower can be a step toward a thermodynamic foundation of LCA.