What concerns agroecosystems, which are typical representatives in the class of anthropogenic ecosystems exploited by Homo sapiens, it is obvious that by increasing the input of artificial energy we increase their (agricultural) production. Note that the increase does not have an upper boundary and can continue infinitely. However, this is not the case, and there are certain limits, determined by the second law of thermodynamics. In other words, we pay the cost for increasing of agricultural productivity, which is a degradation of the physical environment, in particular, soil degradation. As an example, we shall analyze, as a case study, the maize production in Hungary of 1980s.

To start with, we apply the previous results to the case of agroecosystems. By taking into account that only some fraction of the GPP, (1 — k)(1 — r)GPP, participates in the local production of entropy, another fraction, y = k(1 — r)GPP, is exported from the system as a crop yield. Here ris the respiration coefficient and k is the fraction of biomass corresponding to the crop yield y. Note also that the latter and the flow of artificial energy is usually bounded by some linear relation, y = rjW, where q is the so-called Pimentel's coefficient. Then instead of eqn [16] we write d5

GPPo

The agroecosystem will exist for an infinitely long time without degradation if the annual overproduction of entropy will be equal to zero (a = 0). This is a typical situation of the local sustainability.

Therefore, eqn [17] under the condition a = 0 gives us the value of 'limit energy load':

GPPo

[18a which provides sustainability of the agroecosystem, if W< Wsust. Using another form of eqn [18] we get ysust

GPPo

This is an evaluation of some sustainable yield, that is, the maximal crop production, which could be obtained without a degradation of agroecosystem, in other words, in a sustainable manner.

In our case W = 27GJha 1, y = 4.9 ton d.m. per hectare = 73.5GJha—1, q = 2.7, r= 0.4, k = 0.5, s = 0.3. It is natural to take the Hungarian steppe as a reference natural ecosystem with GPP0 = 118GJha—1. By substituting these values into [17] we get uT = 81GJha—1; therefore, to compensate for the environmental degradation we must increase the energy input by three times, when two thirds of it is used only for soil reclamation, pollution control, etc., with no increase in the crop production.

Using eqns [18a] and [18b] we get Wsust = 16GJha—1 and ysust = 2.9 ton d. m. per hectare. It is interesting that the first value is very close to different estimations of the 'limit energy load', 14-15 GJha— , derived from economical considerations or empirically. It is the maximal value of the total anthropogenic impact (including tillage, fertilization, irrigation, pest control, harvesting, grain transportation and drying, etc.) on 1 ha of agricultural land; and if the anthropogenic impact exceeds this limit, an agroecosystem is destroyed (soil acidification and erosion, chemical contamination, etc.).

As to the second value, let us now keep in mind that the contemporary maize yield in the USA is equal to 3 ton; and also after 'black storms of 1930s', the modern agricultural technologies allow us to avoid the strong soil erosion.

Entropy (more correctly the dissipative function, uerT) corresponding to the destruction of one ton of soil in the Hungarian case is uerT = 2.54Gtha— ; then the annual loss of soil per one hectare is uT/uerTk 32. Therefore, the high maize production would cost us 32 ton of soil loss annually. It is obvious that the value of 32 ton per hectare is an extreme value: the actual losses are less, approximately 13-15 ton. This means that also other degradation processes take place, such as environmental pollution, soil acidification (the latter is very significant for Hungary), etc.

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