**3. Eco-exergy**

320 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

which use chemical energy. Nevertheless general rule is the reception of solar energy by green plants via photosynthesis. They assimilate approximately 0,01 – 3 % of energy of falling radiation and, using this energy, create organic matter (*primary production*) from inorganic compounds (water, carbon dioxide, nitrates, phosphates and a lot of minor substances). The by-product of photosynthesis is oxygen. Organisms, creating primary production are called *producers*. Energy, stored in organic matter is used by producers themselves and is dissipated during the processes of plants respiration, growth and reproduction in the form of heat. The remaining energy, accumulated in plant biomass is used by animals to support their structure and functioning. These processes are balanced at global level, as well as in healthy mature ecosystems. The rate of total organic matter production is called *gross primary production*. The difference between *gross primary production* and the rate of decomposition of this substance by plants themselves is called *net primary production*. Organisms, consuming plants (*consumers*) can utilize not more than 10 % of net primary production consumed, the rest being dissipated in the form of heat. Predators (*secondary consumers*) can use not more than 10 % of primary consumers production. The dead bodies of plants and animals, organic wastes, produced by the last etc. are decomposed and reduced to primary inorganic compounds, available for the new cycle of production/destruction by *decomposers* or *reducers* (bacteria and other microorganisms). The rate of total increase of ecosystem biomass (yield) is known as *productivity*. In healthy, mature, balanced ecosystem it is equal to zero (or relation of production to respiration, P/R, is equal to one). So, ecosystem consumes high quality energy of solar radiation, uses part of it to support itself and dissipates the rest in the form of heat, increasing the total entropy of whole system Sun – ecosystem – environment. We have seen the ecosystem is functioning

according to both the first and the second laws of thermodynamics.

1. Mass and energy conservations are valid for ecosystems.

energy—matter input and discharge energy—matter output. 4. Ecosystems have many levels of organization and operate hierarchically.

Previously (Jørgensen & Fath, 2004) eight basic laws of ecology were proposed, but now it was decided to split one of them into three laws (Jørgensen, 2006-2007, 2011). These ten laws

2. All ecosystem processes are irreversible and are accompanied by entropy production

3. All ecosystems are open systems embedded in an environment from which they receive

5. The components in an ecosystem form a complex interactive, self-organizing ecological

6. The carbon based life on Earth, has a characteristic basic biochemistry which all

7. Thermodynamically, carbon-based life has a viability domain determined between

8. After the initial capture of energy across a boundary, ecosystem growth and development is possible by 1) an increase of the physical structure (biomass), 2) an increase of the network (more cycling) or 3) an increase of information embodied in the

9. Biological processes use captured energy (input) to move further from thermodynamic equilibrium and maintain a state of low-entropy and high exergy relative to its

**2.1 Ten basic laws of ecology** 

and exergy destruction.

network.

system.

organisms share.

about 250-350 K.

or Ecological Laws (EL) are listed below.

The exergy of a system is a measure of its deviation from thermodynamic equilibrium with the environment, and represents the maximum capacity of energy to perform useful work as the system proceeds to equilibrium, with irreversibility increasing its entropy at the expense of exergy (Ludovisi, 2009). Taken by itself, the total exergy of an ecosystem is a measure of the change in entropy content from the equilibrium and the actual state (Svirezhev, 2000).

We may distinguish between technological exergy and Eco-Exergy: technological exergy uses the environment as reference state and is useful to find the first class energy (work) that a power plant can produce, Eco-Exergy uses as reference state the same ecosystem with the same temperature and pressure but at thermodynamic - chemical equilibrium (Fig. 1). Below we use the terms exergy and Eco-Exergy as synonymic.

The development and maintenance of the far-from-equilibrium condition of ecosystems is due to the steady storage of free energy into complex organic structures, biosynthesized from simple inorganic compounds. Accordingly, the total exergy of an ecosystem actually reflects the accumulation of biomass into the system, irrespective of the distribution of biogenic matter among ecosystem components. Exergy is a measure of the free energy of a system with contributions from all components including the energy of organisms. The measure for exergy in ecology also includes a factor to weigh the "complexity" of the ecological species. Moving from macroscopic to microscopic information storage, the exergetic contribution due to information grows and becomes even three orders of magnitude higher than the physical one in the more complex living systems. The capacity of packaging information at the molecular level (DNA) that differs from one organism to another can be taken into account using Eco-Exergy function.

Fig. 1. Exergy is calculated for the system relatively to reference environment, Eco-Exergy relatively to the same system at the same temperature and pressure, but as inorganic solution without life and even organic molecules.

Some Applications of Thermodynamics for Ecological Systems 323

where *Ех* – exergy, J; *R* – gas constant, J Mol-1·К-1; *T* – temperature, К; *сi* – concentration of component *i*, Mol; *сi,eq* – cncentration of the same component in the state of thermodynamic equilibrium with environment. Mol; *N* – number of components. The problem is to find value of *сi,eq*. From one hand, exergy of compounds can be calculated on the basis of elementary composition. The disadvantage of this approach consists in that, firstly, input of inorganic components into total exergy of ecosystem is too low, secondly, higher and lower organisms have approximately the same stochiometry (EL 6), so their exergy will be equal, that is in contradiction with information constituent of exergy. From another hand, the value *сi,eq* can be assessed from the probability *Pi,eq* of discovering of component *i* in

If we could find this probability, we can find the ratio of *сi,eq* to current concentration.. As inorganic component с0 prevails in thermodynamic equilibrium state, we can rewrite (2) as:

Chemical potential of dead organic matter (*i* =1) can be found from classic thermodynamics


For biological components (*i* =2, 3, 4, …, N) probability *Pi,eq* is composed from probability of detritus production *P1,eq*, and probability *Pi,а* of genetic information collection to determine

[**1**] (2)

/ , , 0, *Pcc i eq i eq eq* [**1**] (3)

, , 0, *c Pc i eq i eq eq* [**Mol**] (4)

, [**J·Mol-1**] (5)

, , 1, *P PP i eq i eq <sup>а</sup>* (i ≥2). [**1**] (8)

. [**J**] (9)

. [**Mol**] (6)

*eq R T* . [**1**] (7)

thermodynamic equilibrium state:

or

as:

where 

From (3) at *i* =1:

, ,

 

ln( / ) 1 1, 1 1, *RT c c eq eq*

protein structure. Supposing this events independent:

Equation (1) we can rewrite taking into account (4) as:

*N*

exp[ ( ) /( )] 1, 1 1 1, *c c R T eq eq* 

1, 1 0, 1 1, [ / ] exp[ ( ) /( )] *P cc eq eq* 

[ ln( /( )) ( )] , , 0, 0, <sup>0</sup>

*Ex R T c c P c c P c i i i eq eq i i eq eq <sup>i</sup>*

 

*ci eq Pi eq <sup>N</sup>*

, <sup>0</sup>

*c i eq <sup>i</sup>*

Here, we accept the following definition of exergy (according to Jørgensen, 1992; Svirezhev, 2000; Jørgensen & Svirezhev, 2004): *Exergy is the distance between the present state of the system and the state of it in thermodynamic equilibrium with the environment, measured in the units of energy*. It demonstrates the amount of work performed to create a given system from its primary components (in the case of ecological systems — from primary chemical compounds). *Exergy related to the total biomass (structural, specific or normalized exergy) measures the possibility of the ecosystem to accept and utilize external fluxes of energy.* It reflects the degree of ecosystem development or complexity, and has advantages in comparison with the total exergy such as independence from the total biomass of the ecosystem and possibility to serve as an indicator, demonstrating the level of evolutionary development of organisms in the ecosystem.

#### **3.1 Eco-exergy calculation**

According to **Prigogine's theoreme**, an entropy production in every linear system without external influences is decreasing until it reaches minimum at steady state of dynamic equilibrium. Every living system is thermodynamic open system (EL 3) continuously converting potential chemical energy of organic matter into useful energy of creative processes (EL 9) and, in the end of ends, dispose to environment in the form of heat (EL 2). As a result of it, there is no thermodynamic equilibrium in living system. At temperatures, normal for life (see EL 7), living structures are labile and are destructed constantly. To compensate this destruction the permanent internal work in the form of synthesis is fulfilled. These working synthetic processes are processes producing negative entropy (negentropy), they create order with the use of chemical energy of low-entropy energy-rich compounds (consumers and reducers) or low-entropy energy-rich solar radiation (producers). Termination of these processes causes the loss of order, death. Dead body is in thermodynamic equilibrium with maximal entropy.

Exergy is the useful part of energy involved in some process, i.e. the maximal work fulfilled by the system during transit to thermodynamic equilibrium with environment state. This equilibrium means all components to be: 1) inorganic, 2) oxidized to maximum degree, 3) distributed homogenously (there is no gradients in the system). So, if we shall transfer the system into thermodynamic equilibrium with its environment, temperature and pressure will be equal for system and environment, so the only component exergy consists of will be chemical energy. Differences in temperature and pressure between system and environment are small, so we can ignore them in our calculations. The maximal input to exergetic constituent of ecological system will be done due to chemical energy, stored in organic matter and biological structures (Jørgensen et al., 2000; Jørgensen, Fath, 2011; Jørgensen, 2011). Taking into account this concept Eco-Exergy index can be calculated basing on chemical energy: *Σi(c - c,o)Ni*, where *i* – the number of exergy containing components *c*; c – chemical potential of component *c*; *c,o* – chemical potential of component *c* in inorganic state. Eco-Exergy index for the system is calculated by reference of this system to the same system in the form of inorganic soup (i.e. – without life, structure, information, organic matter). The equation for exergy calculation was proposed by S.E. Jørgensen (Mejer & Jørgensen, 1977):

$$\mathbf{Ex} = \mathbf{R} \cdot \mathbf{T} \cdot \sum\_{i=0}^{N} \left[ \mathbf{c}\_{i} \cdot \ln(\mathbf{c}\_{i} \;/\; c\_{i,eq}) - (\mathbf{c}\_{i} - \mathbf{c}\_{i,eq}) \right] J[\mathbf{J}] \tag{1}$$

where *Ех* – exergy, J; *R* – gas constant, J Mol-1·К-1; *T* – temperature, К; *сi* – concentration of component *i*, Mol; *сi,eq* – cncentration of the same component in the state of thermodynamic equilibrium with environment. Mol; *N* – number of components. The problem is to find value of *сi,eq*. From one hand, exergy of compounds can be calculated on the basis of elementary composition. The disadvantage of this approach consists in that, firstly, input of inorganic components into total exergy of ecosystem is too low, secondly, higher and lower organisms have approximately the same stochiometry (EL 6), so their exergy will be equal, that is in contradiction with information constituent of exergy. From another hand, the value *сi,eq* can be assessed from the probability *Pi,eq* of discovering of component *i* in thermodynamic equilibrium state:

$$P\_{i,eq} = \frac{c\_{i,eq}}{\sum\_{\substack{\sum\\i=0}^{N}i\text{,}eq}} \tag{2}$$

If we could find this probability, we can find the ratio of *сi,eq* to current concentration.. As inorganic component с0 prevails in thermodynamic equilibrium state, we can rewrite (2) as:

$$P\_{\rm i,eq} \approx c\_{\rm i,eq} / c\_{\rm 0,eq} \tag{1} \tag{3}$$

or

322 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

Here, we accept the following definition of exergy (according to Jørgensen, 1992; Svirezhev, 2000; Jørgensen & Svirezhev, 2004): *Exergy is the distance between the present state of the system and the state of it in thermodynamic equilibrium with the environment, measured in the units of energy*. It demonstrates the amount of work performed to create a given system from its primary components (in the case of ecological systems — from primary chemical compounds). *Exergy related to the total biomass (structural, specific or normalized exergy) measures the possibility of the ecosystem to accept and utilize external fluxes of energy.* It reflects the degree of ecosystem development or complexity, and has advantages in comparison with the total exergy such as independence from the total biomass of the ecosystem and possibility to serve as an indicator, demonstrating the level of evolutionary development of

According to **Prigogine's theoreme**, an entropy production in every linear system without external influences is decreasing until it reaches minimum at steady state of dynamic equilibrium. Every living system is thermodynamic open system (EL 3) continuously converting potential chemical energy of organic matter into useful energy of creative processes (EL 9) and, in the end of ends, dispose to environment in the form of heat (EL 2). As a result of it, there is no thermodynamic equilibrium in living system. At temperatures, normal for life (see EL 7), living structures are labile and are destructed constantly. To compensate this destruction the permanent internal work in the form of synthesis is fulfilled. These working synthetic processes are processes producing negative entropy (negentropy), they create order with the use of chemical energy of low-entropy energy-rich compounds (consumers and reducers) or low-entropy energy-rich solar radiation (producers). Termination of these processes causes the loss of order, death. Dead body is in

Exergy is the useful part of energy involved in some process, i.e. the maximal work fulfilled by the system during transit to thermodynamic equilibrium with environment state. This equilibrium means all components to be: 1) inorganic, 2) oxidized to maximum degree, 3) distributed homogenously (there is no gradients in the system). So, if we shall transfer the system into thermodynamic equilibrium with its environment, temperature and pressure will be equal for system and environment, so the only component exergy consists of will be chemical energy. Differences in temperature and pressure between system and environment are small, so we can ignore them in our calculations. The maximal input to exergetic constituent of ecological system will be done due to chemical energy, stored in organic matter and biological structures (Jørgensen et al., 2000; Jørgensen, Fath, 2011; Jørgensen, 2011). Taking into account this concept Eco-Exergy index can be calculated basing on

state. Eco-Exergy index for the system is calculated by reference of this system to the same system in the form of inorganic soup (i.e. – without life, structure, information, organic matter). The equation for exergy calculation was proposed by S.E. Jørgensen (Mejer &

*Ex R T c c c c c i i i eq i i eq <sup>i</sup>*

 [ ln( / ) ( )] , , <sup>0</sup> *N*

*c,o)Ni*, where *i* – the number of exergy containing components *c*;

*c,o* – chemical potential of component *c* in inorganic

,[**J**] (1)

c –

organisms in the ecosystem.

**3.1 Eco-exergy calculation** 

chemical energy: *Σi(*

Jørgensen, 1977):

*c -* 

chemical potential of component *c*;

thermodynamic equilibrium with maximal entropy.

$$c\_{\rm i,eq} \approx p\_{\rm i,eq} \cdot c\_{0,eq} \tag{40}$$

Chemical potential of dead organic matter (*i* =1) can be found from classic thermodynamics as:

$$
\mu\_{\rm 1} = \mu\_{\rm 1,eq} + \mathbb{R} \cdot T \cdot \ln(c\_{\rm 1} / c\_{\rm 1,eq}) \,, \tag{5}
$$

where - chemical potential. The difference *μi-μi,eq* is known for detritus. From (5) we see:

$$c\_{1,eq} = c\_1 \cdot \exp[- (\mu\_1 - \mu\_{1,eq}) / (R \cdot T)] \,. \tag{6}$$

From (3) at *i* =1:

$$P\_{1,eq} \approx \left[ \mathbf{c}\_1 \;/ \, c\_{0,eq} \right] \cdot \exp\left[ - (\mu\_1 - \mu\_{1,eq}) / (\mathbf{R} \cdot \mathbf{T}) \right]. \tag{1}$$

For biological components (*i* =2, 3, 4, …, N) probability *Pi,eq* is composed from probability of detritus production *P1,eq*, and probability *Pi,а* of genetic information collection to determine protein structure. Supposing this events independent:

$$P\_{\mathbf{i}, \epsilon q} = P\_{\mathbf{1}, \epsilon q} \cdot P\_{\mathbf{i}, \alpha} \quad \text{ (i \ge 2)}. \tag{8}$$

Equation (1) we can rewrite taking into account (4) as:

$$\mathbf{Ex} \approx \mathbf{R} \cdot \mathbf{T} \cdot \sum\_{i=0}^{N} \left[ \mathbf{c}\_{i} \cdot \ln(\mathbf{c}\_{i} \,/\, (\mathbf{P}\_{i,\text{eq}} \cdot \mathbf{c}\_{0,\text{eq}})) - (\mathbf{c}\_{i} - \mathbf{P}\_{i,\text{eq}} \cdot \mathbf{c}\_{0,\text{eq}}) \right] . \tag{9}$$

Some Applications of Thermodynamics for Ecological Systems 325

2000) *Pi,а* was determined basing on number of informative (structural) genes (each gene

where g – число генов. Then exergy of typical single cell alga (850 genes approximately)

If we relate values of different components of ecosystem exergy to one of detritus (7,34·105), we shall get relative recalculation coefficient *βi*. Corresponding coefficients were calculated for many systematic groups and published (Jørgensen, 1992; Bendoricchio & Jørgensen, 1997; Jørgensen et al., 2000). These coefficients reflect relative complexity of organisms (simpler organisms have lower *β* values). Later, with the use of new genetic data and some indirect methods of *β* values assessment, ratio of non-informative genes to total genes number and others, new list of β was composed and published (Jørgensen et al., 2005;

Therefore, total exergy of ecosystem, based on chemical energy of organic matter (biomass) and information, stored in living organisms (recalculating coefficient β), can be calculated

This exergy now is often called Eco-Exergy (sometimes - exergy index) to distinguish it from

Another indicator of ecosystem state, based on Eco-Exergy, was proposed – structural or specific exergy (structural or specific Eco-Exergy). Structural exergy (*Exstr*) is the exergy related to total biomass (Silow, 1998, 1999, 2006; Xu et al., 1999, 2001, 2004, 2005; Marques et al., 2003; Jørgensen, 2006a). Unlike total exergy it does not depends on biomass and it reflects the ability of ecosystem to accept and utilize the flow of energy from external sources, serving simultaneously as indicator of ecosystem development, its complexity and

> <sup>1</sup> ) <sup>1</sup> () <sup>1</sup> ( *<sup>N</sup>*

*<sup>i</sup> <sup>i</sup> <sup>c</sup> <sup>i</sup>*

We can measure the following aspects of an ecosystem state with the Eco-Exergy: 1) the distance from thermodynamic equilibrium, i.e. general measure of total complexity of ecosystem; 2) structure (biomass and network size) and functions (available information) of ecosystem; 3) ability of ecosystem to survive (expressed via biomass and information of

Structural exergy reflects: 1) efficiency of energy use by organisms; 2) relative information content of ecosystem and, 3) consequently, the ability of ecosystem to regulate interactions

*i*

physical or technological exergy (Marques et al, 2003; Jørgensen, 2006, 2007).

level of evolutionaty development of biological species composed in it.

*N*

*<sup>i</sup> <sup>i</sup> <sup>c</sup> str Ex*

between organisms or groups of organisms.

*i с i с i с*

*<sup>i</sup> <sup>а</sup> <sup>P</sup>* <sup>700</sup> <sup>20</sup> , (*i* ≥2), [**1**] (18)

/ . [**g detritus equivalent m-3**] (20)

. [1] (21)

[**g\*m-3**] (19)

codes the sequence of 700 aminoacids in average) for various taxonomic groups:

*g*

*aa Ex* <sup>5</sup> 102,25 <sup>850700</sup> 20ln <sup>5</sup> 1034,7 lg

Jørgensen, 2007). New *β* values are added every year (table 1).

*N <sup>i</sup> <sup>i</sup> cRTEx*

<sup>1</sup>

can be calculated as:

as:

system).

*TR*

Then:

$$Ex \approx RT \sum\_{i=0}^{N} \left[ c\_{i} (\ln(1/P\_{i,eq}) - \ln(c\_{0,eq}/c\_{i})) - (c\_{i} - P\_{i,eq}c\_{0,eq}) \right] \tag{10}$$

From (3), as сi >> сi,eq , then 1/ Pi,eq ≈ с0,eq / сi,eq >> с0,eq / сi. Consequently

$$\left| \ln(\mathbf{1} \mid P\_{i,\mathbf{q}}) \right| >> \left| \ln(c\_{0,\mathbf{q}} \; / c\_i) \right| \; \tag{1}$$

after that, we can ignore the second logarithm in the sum:

$$\text{Ex} \approx \text{R} \cdot T \cdot \sum\_{i=0}^{N} \left[ c\_{i} \cdot (\ln(1/P\_{i,eq}) - 1) + P\_{i,eq} \cdot c\_{0,eq} \right] \cdot \text{L} \tag{12}$$

Also 1<< ln(1/ Pi,eq) and Pi,eq с0,eq ≈ 0, then:

$$\text{Max} \approx -R \cdot T \cdot \sum\_{i=1}^{N} c\_{i} \cdot \ln P\_{i, \text{eq}} \,. \tag{13}$$

where summation starts from 1, as P0,eq ≈ 1. Taking to (13) Pi,eq from (8) and P1,eq from (7), we have the following expresseion to calculate exergy:

$$\frac{\mathbf{E}\mathbf{x}}{R\cdot T} \approx -\sum\_{i=1}^{N} c\_i \ln\left(\frac{c\_1}{c\_{0,eq}}\right) + \left(\frac{\mu\_1 - \mu\_{1,eq}}{R\cdot T}\right) \sum\_{i=1}^{N} c\_i - \sum\_{i=2}^{N} \left(c\_i \ln(P\_{i,a})\right) \tag{14}$$

In (14) the first sum is insufficient in comparison with the rest two, so:

$$\frac{\text{Ex}}{R \cdot T} \approx \left(\frac{\mu\_1 - \mu\_{1,eq}}{R \cdot T}\right) \cdot \sum\_{i=1}^{N} c\_i - \sum\_{i=2}^{N} \left(c\_i \cdot \ln(P\_{i,\mathcal{Q}})\right) \cdot \quad \text{[Mol]}\tag{15}$$

Exergy in (15) sufficiently depends on organism complexity, as it is connected with information stored in genetic code. This equation can be used to calculate exergy of ecosystem components. If we take detritus (*i* =1), we know that free energy released from it equals approximately 18,7 kJ·g-1. Taking *T*=300 К, *R*=8,31 J·Mol-1·К-1 , and average Mol mass of detritus about 105 g·Mol-1, we obtain the following for detritus exergy in m3 of water:

$$\mathbf{E}\mathbf{x}\_{\rm I} = 18,7 \cdot c\_{\rm I} \qquad \qquad \text{[kJ } \mathbf{m}^{\rm s}\text{]} \qquad \text{or} \quad \frac{\mathbf{E}\mathbf{x}\_{\rm I}}{R \cdot T} = 7,34 \cdot 10^{\rm S} \cdot c\_{\rm I} \quad \text{[g } \mathbf{m}^{\rm s}\text{]} \tag{16}$$

So, we can rewrite (15) as

$$\frac{E\mathbf{x}}{R\cdot T} \approx 7,34\cdot 10^{\mathbf{\tilde{S}}} \cdot c\_{\mathbf{i}} - \sum\_{i=2}^{N} \left( c\_{\mathbf{i}} \cdot \ln(P\_{\mathbf{i},a}) \right) \cdot \qquad \left[ \mathbf{g} \,\mathbf{m}^{3} \right] \tag{17}$$

Now we are to find *Pi,а* – the probability of creation of specific genetic information, characteristic for the organism given. Originally (Jørgensen, 1992, 2002; Jørgensen et al.,

)] , ,0 ())/ ,0 ln() , /1(ln( <sup>0</sup> [ *eq <sup>c</sup> eqi <sup>P</sup> <sup>i</sup> <sup>c</sup> <sup>i</sup> <sup>c</sup> eq <sup>c</sup> eqiP*

From (3), as сi >> сi,eq , then 1/ Pi,eq ≈ с0,eq / сi,eq >> с0,eq / сi. Consequently

*<sup>i</sup> <sup>i</sup> cRTEx* [**J**] (10)

, 0, ln(1 / ) ln( / ) *P cc i eq eq <sup>i</sup>* , [**1**] (11)

. [**J**] (12)

. [**J**] (13)

{**Mol**] (14)

[**g m-3**] (16)

. [**Mol**] (15)

Then:

*N*

Also 1<< ln(1/ Pi,eq) and Pi,eq с0,eq ≈ 0, then:

after that, we can ignore the second logarithm in the sum:

*N*

we have the following expresseion to calculate exergy:

[ (ln(1 / ) 1) )] , , 0, <sup>0</sup>

*N <sup>i</sup> <sup>i</sup> cTREx* , ln 1 

*Ex N c eq N N*

In (14) the first sum is insufficient in comparison with the rest two, so:

*TR*

,11 

*TR Ex*

*TR Ex*

So, we can rewrite (15) as

 

 

*<sup>c</sup> c cP <sup>i</sup> i i ia R T i i c RT <sup>i</sup> eq*

*<sup>i</sup> <sup>i</sup> <sup>c</sup>*

<sup>1</sup> 7,18 <sup>1</sup> *Ex <sup>c</sup>* [**kJ m-3**], or <sup>1</sup>

Now we are to find *Pi,а* – the probability of creation of specific genetic information, characteristic for the organism given. Originally (Jørgensen, 1992, 2002; Jørgensen et al.,

*N <sup>i</sup> aiP <sup>i</sup> <sup>c</sup> <sup>i</sup> <sup>с</sup>*

Exergy in (15) sufficiently depends on organism complexity, as it is connected with information stored in genetic code. This equation can be used to calculate exergy of ecosystem components. If we take detritus (*i* =1), we know that free energy released from it equals approximately 18,7 kJ·g-1. Taking *T*=300 К, *R*=8,31 J·Mol-1·К-1 , and average Mol mass of detritus about 105 g·Mol-1, we obtain the following for detritus exergy in m3 of water:

 

*<sup>N</sup>*

*eq*

*Ex R T c P P c i i eq i eq eq <sup>i</sup>* 

*eqi P*

where summation starts from 1, as P0,eq ≈ 1. Taking to (13) Pi,eq from (8) and P1,eq from (7),

1 1, <sup>1</sup> ln ( ln( )) , <sup>1</sup> 1 2 0,

 

*<sup>i</sup> ai <sup>P</sup> <sup>i</sup> <sup>c</sup> <sup>N</sup>*

<sup>2</sup> )) , ln(( <sup>1</sup>

*TR*

<sup>5</sup> 1034,7 <sup>1</sup> *<sup>с</sup>*

*Ex*

<sup>2</sup> )) , ln(( <sup>5</sup> 1034,7 . [**g m-3**] (17)

2000) *Pi,а* was determined basing on number of informative (structural) genes (each gene codes the sequence of 700 aminoacids in average) for various taxonomic groups:

$$P\_{\mathbf{i},a} = 20 \stackrel{-700 \,\mathrm{g}}{\quad} \quad \text{( $i \gg 2$ )}, \tag{1}$$

where g – число генов. Then exergy of typical single cell alga (850 genes approximately) can be calculated as:

$$\frac{Ex\_{al\lg a}}{R \cdot T} \approx 7,34 \cdot 10^5 \, c\_{\hat{l}} - c\_{\hat{l}} \ln 20^{-700 \times 850} \approx 25,2 \cdot 10^5 \, c\_{\hat{l}} \, \text{ [g}^\ast \text{m}^\ast\text{]} \tag{19}$$

If we relate values of different components of ecosystem exergy to one of detritus (7,34·105), we shall get relative recalculation coefficient *βi*. Corresponding coefficients were calculated for many systematic groups and published (Jørgensen, 1992; Bendoricchio & Jørgensen, 1997; Jørgensen et al., 2000). These coefficients reflect relative complexity of organisms (simpler organisms have lower *β* values). Later, with the use of new genetic data and some indirect methods of *β* values assessment, ratio of non-informative genes to total genes number and others, new list of β was composed and published (Jørgensen et al., 2005; Jørgensen, 2007). New *β* values are added every year (table 1).

Therefore, total exergy of ecosystem, based on chemical energy of organic matter (biomass) and information, stored in living organisms (recalculating coefficient β), can be calculated as:

$$\text{Ext}\,\langle RT\,\,=\sum\_{\mathbf{i}=\mathbf{l}}^{N}\mathbf{c}\_{\mathbf{i}}\cdot\boldsymbol{\beta}\_{\mathbf{i}}\,.\quad \text{[ $\mathbf{g}$ -detittus equivalent  $\mathbf{m}^{3}$ ]}\tag{20}$$

This exergy now is often called Eco-Exergy (sometimes - exergy index) to distinguish it from physical or technological exergy (Marques et al, 2003; Jørgensen, 2006, 2007).

Another indicator of ecosystem state, based on Eco-Exergy, was proposed – structural or specific exergy (structural or specific Eco-Exergy). Structural exergy (*Exstr*) is the exergy related to total biomass (Silow, 1998, 1999, 2006; Xu et al., 1999, 2001, 2004, 2005; Marques et al., 2003; Jørgensen, 2006a). Unlike total exergy it does not depends on biomass and it reflects the ability of ecosystem to accept and utilize the flow of energy from external sources, serving simultaneously as indicator of ecosystem development, its complexity and level of evolutionaty development of biological species composed in it.

$$\mathbf{E}\mathbf{x}\_{\rm Str} = (\sum\_{i=1}^{N} \mathbf{c}\_{\hat{\mathbf{l}}} \cdot \boldsymbol{\beta}\_{\hat{\mathbf{l}}}) \cdot (\sum\_{i=1}^{N} \mathbf{c}\_{\hat{\mathbf{l}}})^{-1}. \tag{11}$$

We can measure the following aspects of an ecosystem state with the Eco-Exergy: 1) the distance from thermodynamic equilibrium, i.e. general measure of total complexity of ecosystem; 2) structure (biomass and network size) and functions (available information) of ecosystem; 3) ability of ecosystem to survive (expressed via biomass and information of system).

Structural exergy reflects: 1) efficiency of energy use by organisms; 2) relative information content of ecosystem and, 3) consequently, the ability of ecosystem to regulate interactions between organisms or groups of organisms.

Some Applications of Thermodynamics for Ecological Systems 327

hypothesis that an ecosystem can coordinate the most complex behaviour in the case of high level of exergy of the systems at the edge of oscillation before entering into the chaotic situation (Mandal et al., 2007). The thermodynamic notion of exergy was shown to give better insight both to the patterns of nonlinear ecosystem behaviour and to comparison of

There are very few researches devoted to analysis of plankton communities with the aid of exergy. The implications of body sizes of phytoplankton and zooplankton for total system dynamics by optimizing exergy as a goal function for system performance indicator with mathematical models have been analyzed (Ray et al., 2001). A structurally dynamic model based on phosphorus nutrient limitation has been developed for Lake Mogan located nearby Ankara, Turkey. Exergy was applied as a goal function to consider the dynamic adaptation and the seasonality of plankton species (e.g., size shifts) (Zhang et

The ecosystem of the North Sea integrity was approved to be reflected in exergy capture, storage capacity, cycling, matter losses, and heterogeneity (the diatom/non-diatom ratio of planktonic algae was used) with ecosystem model. Its feasibility was assessed as an ecosystem model of the North Sea, for the Elbe plume, after prior satisfactory calibration. The modeling effort suggested that drastic nutrient load reduction from the Elbe alone would have a limited effect on the larger German Bight: even a 60% reduction scenario

More representative and multiple are applications of exergy to benthos communities. Exergy was used in optimization models of phytobenthos (Nielsen, 1997). Exergy concept allowed the finding of the best adapted water plants species in a given environmental condition and to explain in a satisfactory way the observed distributions of them in the

Exergy storage was estimated for benthic communities of sandy and muddy bottoms of the North Adriatic Sea subjected to experimental disturbance, induced by means of a controlled trawl fishing haul. The results showed a decrease of local exergy content in the disturbed area, with the minimum, both in sandy and muddy bottom, one month after the experimental disturbance. The exergy of the benthic community increased to the reference level, i.e., the surrounding control area, in accordance with the proposed hypothesis on the

The changes of exergy and specific exergy were studied with data of benthic macrofauna in the Mondego estuary (Western Portugal). Estimates for the exergy indices provided useful indications for the evaluation of environmental impact due to the eutrophication process

Export of exergy was estimated for benthic communities on the South-Western Atlantic Coast of France. This export was mainly composed of the migration of grazing fish during the warm season, and of cultivated bivalves during the cold season (Leguerrier et al.,

In the following study a self-organizing map for patterning exergy of benthic macroinvertebrate communities of 650 sampling sites in the Netherlands, including 855 species was implemented. Using these datasets, authors have calculated exergy of five trophic functional groups for each sampling site on the basis of the biomass data. Exergy of

would only lead to moderate changes in all five indicators (Windhorst et al., 2005).

dynamics of exergy storage during a systems' development (Libralato et al., 2006).

the patterns in ecological modelling (Svirezhev & Steinbom, 2001).

**3.2.2 Eco-exergy and aquatic ecology** 

Lagoon of Venice, Italy (Coffaro et al., 1997).

al, 2003a, b).

(Fonseka et al., 2002).

2007).


Table 1. Exergy/Biomass Conversion factors for different groups of organisms, after Silow & Mokry, 2010

### **3.2 Eco-exergy and structural exergy applications in ecology and environmental science**

#### **3.2.1 Eco-exergy in theoretical ecology and in aquatic ecology**

We have seen above exergy approach was demonstrated to be very fruitful during the analysis of the application of thermodynamic principles and laws to the main fundamental concepts of ecology at the end of the XX century. The analysis of three thermodynamic laws expressions in ecological rules together with exergy analysis led to formulation of the 10 Ecological Laws, in particular the Fourth (Ecological) Law of Thermodynamics, EL9 (Patten et al., 1997; Jørgensen et al., 1999; Straškraba et al., 1999; Jørgensen, 2006b).

Non-equilibrium thermodynamics models based on the concept of exergy provided a common basis for representing many aspects of ecosystem development and response to environmental impacts as a single measure (Pykh et al., 2000). The use of exergy made possible the investigation of the flows of an ecosystem in terms of exergy and to arrange the system as a hierarchically ordered sequence of systems, thermodynamically embedded in each other (Nielsen, 2000). Experiments with mathematical models supported the hypothesis that an ecosystem can coordinate the most complex behaviour in the case of high level of exergy of the systems at the edge of oscillation before entering into the chaotic situation (Mandal et al., 2007). The thermodynamic notion of exergy was shown to give better insight both to the patterns of nonlinear ecosystem behaviour and to comparison of the patterns in ecological modelling (Svirezhev & Steinbom, 2001).
