## Emergy Algebra

As stated above, emergy analysis obeys a logic of memorization and therefore needs its own algebra, that is summarized in four main rules, which according to Brown are:

1. All source emergy to a process is assigned to the process's output (Emk):

where Ej is the energy of the ith component and

2. By-products of a process have the total emergy assigned to each pathway.

3. When a pathway splits, the emergy assigned to each branch is based on its percentage of the total energy flow on the pathway (the two products are called splits).

4. Emergy cannot be counted twice in a system: (a) emergy in feedbacks is not counted twice; (b) when emergy ofby-products is summed, it cannot be greater than the source emergy from which it was derived.

It follows that the transformities of two (or more) splits are identical, while their emergy contents are generally different (unless energy is distributed equally among the splits); on the contrary, the transformities of co-products are generally different (unless the same amount of energy went into the various co-products).

The first emergy rule indicates that it is necessary to know the emergy of the inputs in order to calculate the emergy of the output. Apart from the sun, that has a transformity of 1 by definition, it is necessary to calculate the transformity or emergy of natural resources. Emergy accounting starts with an evaluation of the Earth's emergy processes.

The reference baseline (that represents the reference for the emergy calculations) is 15.83 x 1024sej yr_1. Once the emergy of the main natural flows was calculated, it became possible to calculate the emergy of many resources, from minerals to fossil fuels. The first emergy studies took 9.44 x 1024sej yr_1as baseline and can be updated by multiplying the transformities used in the emergy evaluation by 1.68.

Today in the literature it is possible to find a great many transformities. Many are periodically revised by emergy scientists in special publications called folios.

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