Wch RT X lnCiCqi92

Strictly speaking, the above-obtained formula is applicable to sufficiently smooth continuous processes, whereas the real process is saw-tooth with 1-year periodicity. Therefore, in order to study slow dynamics of the entropy overproduction, we have to know how to average the function a(t) within a 1-year interval.

Let an anthropogenic pressure begin to act on the natural ecosystem at an initial moment t0 when C(t0) = C0. If only the entropy pump "sucks out" entropy from the system then the rate of the entropy production will be dS=f) Ry / CJtA dCi r(t)GPP(t) + D(t) GPPp(t)

where r(t) is the respiration coefficient and D(t) is the rate of dead organics' decomposition within a 1-year interval. By integrating with respect to time and applying the Mean Value Theorem we obtain

We assume that the temperature T remains constant in the course of the entire period of an anthropogenic impact and is equal to t. We consider a quasi-stationary process in the sense that [1 — r(i)]GPP(i) < D(t), i.e. there is a dynamic equilibrium between the formation of the new biomass and the decomposition of the dead organic matter. Then the total overproduction of entropy in the course of the entire period of an anthropogenic impact will be equal to

St = S(to + t) - S(to) = T [Wf + Wch + (GPP)t - GPPot] ,

where Wf = J"0Wf(t +t0)dt is the total energy load and {GPP) = 1/rJ"SGPP(t + t0)dr is the mean gross primary production averaged over the interval of anthropogenic impact. The total chemical load can be represented as

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