## Entropy Balance in Elementary Ecosystems

From the thermodynamic point of view, any ecosystem is an open system. An ecosystem being in a 'climax' state corresponds to a dynamic equilibrium, in which the internal production of entropy is balanced by the entropic outflow to the environment.

An 'elementary ecosystem' is the area unit of land, covered by some type of vegetation, which is properly the main part of any terrestrial ecosystem, and upper layer of soil with litter, in which oOM is decomposed. We neglect horizontal exchange flows of matter, energy, and entropy between this and other ecosystems.

The equation of energy balance for this area is R = hevp^W + Qturb + hoOMGPP (see also Energy Flows in the Biosphere). Here hevp = 2462J g—1 H2O is the specific enthalpy of evaporation, qW is the flow of evapotranspiration, Qis the turbulent heat flow, transporting heat from the surface into the atmosphere, hDOM = 17.4 kJ g— is the specific enthalpy of DOM, and GPP is the gross primary production (in g d.w.). Oxidation of biomass (respiration and decomposition of DOM) gives an additional source of heat, therefore the left side of the balance equation has to be R + (Qmet + Qdec), where Qmet is a metabolic heat and Qdec is heat releasing in the process of decomposition.

Let us group items of the radiative balance into two classes (in square brackets), which differ by values of their elements: [R — h„qW — Qturb] + [Qmet + Qdec — GPP] = 0, where the difference may constitute a few orders. For instance, the energy acting in the process of evapotranspiration is higher by two orders of magnitude than the energy of photosynthesis. Then we can equate each of the brackets to zero (it is the so-called 'asymptotic splitting': [R — hev^W — Qturb] = 0 and [Qmet + Qdec — GPP] = 0.

We assume that the fulfilment of the first equality provides the existence of some 'thermostat', which should be called the 'environment'. Then the fulfilment of the second equality is determined by a consistency of the processes of production, on the one hand, and metabolism of plants and decomposition of DOM in litter and soil, on the other.

In accordance with a standard definition, the internal production of entropy is equal to dS/dt — Qox/T, where Tis the system temperature, and Qox is the heat generated by the system. The total heat production is a result of two processes: metabolism or respiration (Qmet) and decomposition of DOM (Qdec). Since these processes can be considered as a burning of corresponding amount of organic matter, then the values of Qmet and Q-6c can be also expressed in enthalpy's units. Thus, diS/dt — (Qmet + Qdec)/T. The mean annual temperature at the surface of given site is the system temperature.

Since the equality [Qmet + Qdec — GPP] = 0 must hold, then diS/dt — GPP/T. At the dynamic equilibrium the internal entropy production must be compensated by the entropy export from the system, so that diS

deS dt

where |deS/dt| is so-called 'entropy pump', which 'sucks' the redundant entropy (that is existing in the system for a long time), out of the ecosystem. We assume the local climatic, hydrological, soil, and other environmental conditions are adjusted in such a way that only one natural ecosystem corresponding specifically to these conditions can exist at this site and be in dynamic equilibrium. This is a concept of 'entropy pump'.

Any natural ecosystem is in dynamic equilibrium if and only if the internal entropy production within the system is balanced by an entropic outflow from the system to its environment (the 'entropy pump' is working). Suppose that additional inflows of artificial energy (energy load, Wae) and chemical substances (chemical load, Wch) start entering into the system. This is a typical impact of industry (or, in a broader sense, technological civilization) and industrialized agriculture on the environment. The internal production of entropy by the 'disturbed' ecosystem is given by diS 1 r

where W = Wae + Wch is the total anthropogenic impact. Since a certain part of the entropy is released by the

'entropy pump' with power |deS/dt| = GPP0/T, where GPP0 is the gross primary production of undisturbed 'wild' ecosystem located at a given point, then the total entropy balance is given by

dt T

Under the anthropogenic pressure, the system moves toward a new state, gaining the ability to perform some work, then it returns to the initial state, performing the work and producing the entropy. This is a typical two-time working cycle of a thermodynamic machine called an 'elementary ecosystem'.

If this system tends to some stable dynamic equilibrium with respect to W (Weq = W*) and, in addition, satisfies to Prigogine's theorem, then GPP(W*) + W* = GPP'o and GPP( W) + W ! min at W* = 0. Here

GPP9o is a new value of the power of 'entropy pump', corresponding to a new equilibrium, which is established in the process of succession from natural to 'anthropogenic' ecosystem. Unfortunately, the proper time of this transition is rather long, and often the transition is not successfully finished (e.g., the 'old field' succession recovers a structure ofpre-anthropogenic natural ecosystem, and does it very fast).

As a rule, the decrease in entropy, obtained at the first stage ofthe cycle, does not compensate its increase at the second stage. The further destiny of this 'superfluous' entropy could be different: (1) it is accumulated by the system, the system (in particular, its environment) degrades, and after a while, dies; (2) entropy may be exported from the system, the initial state is reestablished, and the system is again ready for the next cycle. The latter strategy may be realized by means of an import of additional low-entropy energy that could be used for the system restoration: soil reclamation, pollution control, or generally speaking, ecological technologies, etc. In other words, this refers to the so-called 'ecological management'. Using such entropy calculation, we can estimate the necessary investments (in energy units).

Unfortunately, there is a 'third alternative' to restore the initial state: to divide the system on two parts - a proper biological community and its abiotic environment, pumping over the superfluous entropy from one to another. In other words, we try to resolve the problem at the expense of environmental degradation. Note that the value of entropy excess a could be used as a measure ofthe latter, or, as the entropy fee which has to be paid by society (actually suffering from the degradation of environment) for modern industrial technologies.

From the thermodynamic point of view, the environmental degradation leading to a decrease in the GPP is a typical system's reaction tending the internal entropy production to decrease (Prigogine's theorem and Le Chatelier's principle), while it may be considered as a disaster from the anthropocentric position. Thus, in order to avoid the anthropogenic disaster, we have to compensate the positive increment of entropy at each working cycle of this machine.

All these concepts are visibly illustrated in the case of agroecosystems.

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