# Thermodynamics in Ecology—An Introductory Review

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## Abstract

**:**

## 1. Introduction

## 2. History

## 3. The Thermodynamic Laws

#### 3.1. The First Law of Thermodynamics

#### 3.2. The Second Law of Thermodynamics

_{i}are the probabilities of different possible, distinguishable elements. Under conditions close to equilibrium, systems, like ideal gases, will move to a distribution of particles having the highest probability or highest entropy. This may in a slightly oversimplified version be illustrated by Figure 3.

_{i}is the molar chemical potential and n

_{i}the moles of type/element i, respectively. This form seems to be most relevant to biological systems. The importance to ecological systems will be described later.

## 4. Some Fundamental Concepts

- (a)
- the various types of systems and
- (b)
- the relations between energy form and quality

#### 4.1. Types of Systems

#### 4.1.1. Isolated Systems—Or Adiabatic Systems

#### 4.1.2. Closed Systems

#### 4.1.3. Open Systems

#### 4.2. Energy: Form and Quality

## 5. Far from Equilibrium Thermodynamics

#### 5.1. Dissipative Structures

_{i}S is the entropy change caused by internal processes, while d

_{e}S is caused by external exchanges. Whereas d

_{i}S is always positive as dictated by the second law, the second term of the equation, d

_{e}S, may be negative and numerically larger than d

_{i}S, which allows the resulting entropy balance of the system also to be negative.

_{e}S has to be even less than the negative of the internal entropy production. Under these conditions living structures may occur and even grow. In the case of equality, a thermodynamic balance or homeostasis exists.

_{e}S, does not compensate for the entropy created by internal processes, the living structures or system under consideration may exist only until internal resources have been used up, i.e., over a limited time span. Otherwise, this thermodynamic condition eventually means death. Various examples of life strategies to cope with such temporal imbalances can be found throughout biology among both plants and animals, e.g., hibernation of seeds, hibernation in bears.

#### 5.2. Minimum Specific Dissipation

_{i}S and d

_{e}S may be designated as the entropy production and the entropy flow term, respectively. Failure to distinguish between the two formulations (i.e., entropy production vs, entropy production density) may be the cause of many of the ongoing discussions and controversies between the various ways of applying thermodynamics to ecosystems. This is valid in particular when considering arguments around maximization and minimization of entropy productions.

#### 5.3. Evolution through Instabilities

#### 5.4. An Ecological Law of Thermodynamics?

## 6. Exergetics

#### 6.1. Thermodynamic Information

_{eq}is the entropy at thermodynamic equilibrium (maximal entropy) and S

_{state}is the actual entropy state of the system. It is seen that exergy must be a positive term, that it has the units of energy, and that it is a measure of the system’s distance from some thermodynamic equilibrium. As mentioned, this is not necessarily equilibrium in the classical sense. For biological systems it is probably more relevant to consider a reference level as the surrounding environment. This may be illustrated by Figure 16. The system reaches a different distribution of microstates, p

_{i}, differing from the one it would have at thermodynamic equilibrium or the environment, p

_{i}

_{,0}, and therefore also has another entropy state. The entropy state reached will differ depending on the path taken.

#### 6.2. Exergy Optimization

- (1)
- Living systems—all biological systems as well as ecosystems are open systems in the sense that they import and exchange both energy and matter with the environment in which they are embedded
- (2)
- As the imported energy through metabolism is used for driving irreversible processes it is at the same time
- (a)
- converted into lower quality/value energy forms exporting dissipated energy to the surrounding environment, and/or
- (b)
- built into intermediate, chemical energy compounds, thereby

- (3)
- Building up structures through processes such as auto-poiesis, autocatalysis, and self-organization driven by the energy and material gradient of the system.

## 7. Application of Thermodynamics to Ecology

#### 7.1. Entropy of Biological Systems

#### 7.1.1. Entropy and Developmental Biology

#### 7.1.2. Entropy and Organisms

#### 7.1.3. Entropy of Ecosystems

#### 7.1.4. Other Studies

#### 7.2. Exergy and Ecosystems

#### 7.3. Exergy Storage

#### 7.3.1. The Classical Approach

_{0}and Ex

_{0}, respectively. As both these reference values by definition are 0 (zero) they have been omitted from the equations).

_{i}is the concentration of a given chemical element in various compartments of the system. The equation is argued to be valid for systems with inorganic net inflow and passive organic outflow [38].

#### 7.3.2. Internal Exergy

_{i}are the fractions of chemical elements in the compartments of the system. The expression can in fact be shown to be equal the above expression without the relations to the external. The difference between the above presented approaches was analyzed through the thesis work of Nielsen [190,230,294,295,296,297] and the variation was found to differ only slightly and in particular when structural shifts occurred in the ecosystems under consideration.

#### 7.3.3. Exergy Indices

_{eq,i}(or x

_{eq,i}in the latter). In order to explain this, let us try to translate this term into ordinary chemical language. What we seek to express through this equation is: the probability of finding organic compounds, eventually put together as an organism (or several types of organisms of the ecosystem) but at a state of thermodynamic equilibrium or in the primordial soup. In the equations this in turn would need to be expressed as its “hypothetical” concentration under the same conditions. A conflict arises since no life is assumed to exist under the conditions of thermodynamic equilibrium. This creates the first problem. The probabilities are extremely low and the first half of the equation becomes dominant in the calculation. Furthermore, they were estimated to be so low, (around 10

^{−50}) that they were hard to accept since such values could neither be proved nor measured.

_{eq,i}(or x

_{eq,i}). This was not considered to be quite satisfactory for the reasons just described, but mainly due to the problems related to the unrealistic possibility of life to exist at the reference level of thermodynamic equilibrium.

^{−1}[234,235] thus giving a basic value to be used in the formulation of another possible reference level.

_{i}, to be multiplied with the biomass of each of the compartments, thus this new exergy index, often referred to as is defined as:

_{i}is the biomass, expressed as concentration, of compartment i.

#### 7.4. Application of Exergy Storage

#### 7.4.1. Observation and Evaluation

#### 7.4.2. Goal Functions

#### 7.4.3. Comparisons to Other Ecosystem Theories

#### 7.5. Exergy Degradation

“When an isolated (sic!) system performs a process after the removal of a series of internal constraints, it will reach a unique state of equilibrium: this state of equilibrium is independent of the order in which the constraints are removed”.

“As systems are moved away from equilibrium, they will utilize all avenues available to counter/resist the applied gradients. As the applied gradients increase, so does the system’s ability to oppose further the movement from equilibrium”[39]

#### 7.6. Results of Exergy Degradation

#### 7.6.1. Remote Sensing, Global

#### 7.6.2. Landscapes and Regional Scale

#### 7.7. Storage or Degradation

## 8. Discussion and Future

- (a)
- Problems related to science of physics - the science of thermodynamics and particular its extension into the far-from-equilibrium domain of conglomerate systems is still a relatively new discipline and in many ways in opposition to the Newtonian and determinist worldview still held by many scientists. As a consequence, many discussions are still taking place within the area.
- (b)
- Problems of transfer—whenever a scientific theory is transferred (reduced) to another area problems are to be expected. Does the theory, or the transfer of it, hold at all, for the whole set of systems or for parts of it, i.e., is the transfer to new conditions or domains valid?
- (c)
- Problems of application—after theoretical transfer problems of practical application appear. This in brief deals with both problems of measuring as well as how to proof the validity of such theories after transfer. Insofar, we must take much of the above statements as conjectures although much evidence of at least some important thermodynamic features of ecosystems has been gathered.

- (a)
- Most important to establishing a connection between thermodynamics and biology seems to be the necessary extension of the validity of thermodynamics into far-from-equilibrium conditions. The traditional point taken, stated in a very simplified form, would argue that thermodynamics only deals with ideal gases at conditions close to thermodynamic equilibrium. Whatever variety, or nuances, of this attitude will be taken, it will bring the transfer and application of thermodynamics into deep trouble. If one stands hard on the point that thermodynamics as science is valid only to “ideal gases close to (real) thermodynamic equilibrium, not only will the situation in biology and ecology be in deep trouble, so would a large part of the physical and engineering sciences as the universality and role of the second law together with its penetration into all other physical disciplines vanishes.

- (b)
- With the last points we implicitly address the problem of transfer to biological sciences and also to ecology as presented above. At this point it should be clear that not all problems come from the transfer alone, they existed already.

- (c)
- This brings us back to yet another problem in the application of the exergy principle. None of the above presented approaches is able to measure entropy, exergy or any kind of thermodynamic balance, directly. We have no entropy syringe or exergy meter to put on our system. This means that we are not able to fulfil the Cartesian demand of “making everything measurable”. In short, we will be forced to work with inductive or abductive based methods. Except, if we accept indirect measurements, calculation or modelling as valid methods for this purpose, which seems to be our only way out of this dilemma at the moment.

## 9. Summary and Conclusions

- (a)
- Thermodynamics in organizational levels and hierarchy perspectives

- (b)
- Thermodynamics of Earth and the biosphere

- (c)
- Entropy production vs. entropy state, exergy storage

- (d)
- Thermodynamic synergism

- (e)
- Ecological time-space thermodynamics

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Overview over some historical events leading to the application of thermodynamics and exergy into ecology. The scheme has been divided into three areas, (1) one for the development of thermodynamics within physics, (2) a second line linking thermodynamics to biology, and (3) a third line showing important events in the development of the relation between ecology and society as we see it today. An attempt has been made to place authors in accordance with their respective areas of research efforts with indication of approximate time of major contributions.

**Figure 2.**(

**a**) A universal energy diagram according to E.P. Odum [2,168]. The components are: ingested energy, I, energy not used, NU, energy assimilated, A, production, P, respiration, R, growth, G, energy stored, S, and energy excreted, E. All functions carried out by biomass, B. (

**b**) An energy flow diagram for a marine bay ecosystem showing the energies flowing through the grazing chain in the water column and entering the sediments, respectively. Both diagrams have been redrawn and modified after Odum [2].

**Figure 3.**Two systems, the one more complicated than the other, both moving towards thermodynamic equilibrium, i.e., a state of more equal and more probable distribution, ending in a state of maximum randomness. Thus, entropy goes to maximum as elements are reaching the distribution of highest probability as dictated by the second law of thermodynamics, as is the situation for an isolated system (figure oversimplified).

**Figure 4.**An isolated system has a boundary towards its surrounding environment, which is totally closed to exchanges of both energy and materials between the two compartments.

**Figure 5.**Closed systems have boundaries which are open to and may receive or exchange energy fluxes. At the same time, the materials potentially enclosed in the system at initial conditions must remain constant. Meanwhile, this still leaves the possibility of the elements to be structured or (self-)organized in various, more or less “sensible” ways according to other physicals laws, like in it is the case with some physical systems like the advective Bénard-cells mentioned in the text.

**Figure 6.**Open systems are open to both energy and material fluxes. They may use the energy and material fluxes received to build-up and organize matter or compositional elements, distributing them in still more advanced patterns and even have the capability to grow in size. Energy in general needs to leave the system as dictated by the second law always, e.g., the heat formed by dissipative processes, for instance through metabolism. The dissipated energy must disperse to the environment and this surrounding reservoir in turn must be able to tolerate this [138]. That matter leaves is not a necessity unless we for instance think of degraded compounds which otherwise might be harmful to organisms, c.f. the role of kidneys. Meanwhile, for many biological systems exchange pattern will be determined by ecological roles or by forcing functions.

**Figure 7.**Transformation of energy through “Brillouin’s cascade”. Energy is always transformed in one direction only, from high quality, like radiation, to a sequentially lower quality, ending up as its lowest quality form, namely heat, i.e., ending up as dissipated energy as result of the irreversibility of processes.

**Figure 8.**Biological systems move away from thermodynamic equilibrium either (1) as is the case with autotrophs by photosynthesis, i.e., input of high quality energy through solar radiation, or (2) by uptake or build-up of complex molecules which is possible by adding up several energy bundles of intermediate quality via energy carriers, e.g., ATP. In the ecosystem this process is ultimately driven by a supply of chemical energy from the autotrophic organisms, most other processes are driven by this chemical energy, which supplies metabolic and respiratory processes (redrawn and modified from Müller and Nielsen, [178].

**Figure 9.**Open systems use the energy flowing through them to create structures which deviate from thermodynamic equilibrium in more and more complex manners. The sorting of elements among the molecules in cells and organisms may be seen as an example of this function of life. (Figure oversimplified and not random enough).

**Figure 10.**According to Prigogine and co-workers far-from-equilibrium systems may be understood also as dissipative structures where the total entropy change, dS, is a consequence of internal entropy production, d

_{i}S, as well as exchanges with the surroundings, d

_{e}S. Drawing modified from Prigogine [75].

**Figure 11.**The figure shows the entropy production as a function of time for a system under development. As the system reaches a dynamic equilibrium it enters a state of minimum dissipation and entropy production levels off (redrawn and modified after Prigogine [73].

**Figure 12.**Stable periods with minimum dissipation will eventually lead to instabilities and the possibility for new stable structures to occur. More stable states may coexist depending on the availability of resources and competition for the same, i.e., the external as well as internal constraints on the system.

**Figure 13.**A sequence of minimum dissipation periods, instabilities and bifurcations may be seen as an explanation of serial evolution of biological systems—a so-called habit that is taken on at more levels of hierarchy.

**Figure 14.**Ecosystems, during their development, show distinct changes in species composition and as a consequence sometimes the whole structure of the trophic network gets affected. This is traditionally seen as a response to changes in factors affecting and driving the system (often in ecological modelling referred to as forcing or control functions) but may eventually also depend on the intrinsic properties of possible organisms. As a consequence, and in order to meet the changes, the ecosystems may react on several levels of hierarchy, e.g., genotype, phenotype or ecotype.

**Figure 15.**The exergy balance of the system may serve to make the role of various types of energy use more explicit. Exergy may enter over the boundaries, Ex

_{imp}, like photosynthesis or import of material via forcing functions. Exergy may enter or leave a subsystem from or to other systems parts, Ex

_{ij}and Ex

_{jk}, respectively. Part of the exergy will always be dissipated and lost and will not be available to any system, Ex

_{diss}(actually not exergy any longer, but kept open for accounting).

**Figure 16.**The thermodynamic state, S (p

_{i}), of a living system is moved away from thermodynamic equilibrium to a far from equilibrium state. In calculation of exergy the reference level is often set to that of thermodynamic equilibrium S

_{eq}or S

_{pi}

_{,0}.

**Figure 17.**A trophic network illustrating a typical aquatic ecosystem with internal recycling through a detritus and bacterial compartment. The flows are translated into exergy relationships, see Figure 15, making it possible to track the energy conversion and dissipation throughout the system. (redrawn from Nielsen and Ulanowicz [232].

**Figure 18.**The ecosystem as it evolves will move along a thermodynamic path composed of a sequence of possible thermodynamic (optimal) solutions to the condition met from the surroundings (redrawn and modified from Kay [15].

**Figure 19.**The ecosystem tends to evolve towards an optimum operating point. When subsided to small perturbations the system will stay at or close to its optimum. Major disturbances will move the system to a new optimum operating point in accordance with changes induced. The new path may be found via bifurcations or on other branches through catastrophic events (redrawn and modified from Kay and Schneider [15].

**Figure 20.**As ecosystems grow and develop, here interpreted as an increase in exergy storage, their efficiency, expressed as percentage of incoming exergy captured, levels off to a seemingly constant level (redrawn and modified from Jørgensen, [7]. Meanwhile, the systems may differ in other parameters such as bio-diversity.

**Figure 21.**In the calculation of exergy for a biological systems on may choose between different sensible reference levels, detritus level, organic or inorganic level, often referred to as the “Oparinian Ocean” or primordial soup, etc. The exergy contribution from choosing between the various levels is considered to play only a minor part in the calculation of the total exergy of the state. The difference between various reference levels is exaggerated for clarity but is really being considered to contribute only little in the calculation of the total (eco-)exergy state of the system under consideration.

**Table 1.**Examples of thermodynamic properties of ecosystem hypothesized to perform with a pattern-like change during ecosystem development. Some of the properties may be used as indicators of ecosystem state or as candidates of goal functions for instance in ecological modelling.

Variant | Origin (Major References) | Remarks |
---|---|---|

phenomenology of 24 principles during undisturbed development of naturals systems towards climax society | Odum, E.P. [1,2] | Principle 23 and 24 are referring to decrease in entropy and increase in information of the ecosystem, respectively |

emergent properties | Odum, E.P. [21] | The study of emergent properties of ecosystems is proposed as research strategy |

maximum (useful) power | Odum, H.T. [3,22,23,24] | The idea originating in Lotka’s papers from the early 1920′ies |

eMergy | Odum, H.T. [25,26] | |

minimum dissipation/entropy | Mauersberger, P. [27,28,29,30] | minimum dissipation as extremal principle for aquatic ecosystems |

entropy | Aoki, I. [31,32,33,34,35,36] | |

maximum exergy (storage) | Jørgensen, S.E. [7,37,38] | the exergy function derived was shown to relate to buffer capacity and proposed as a holistic indicator and goal function— exergy optimization of ecosystems recently proposed as an ecological law of thermodynamics |

maximum exergy degradation | Schneider, E & Kay, J.J. [14,15,39,40,41] | maximum exergy degradation proposed as driving mechanism, exergy degradation as indicator of ecosystem integrity |

maximum entropy production | Martyushev [42,43] | validity of maximum entropy production from physics to biology |

Ascendency | Ulanowicz, R.E. [5,6,44,45] | ecosystems as they grow and develop show an increase in ascendency, flows serve as orientor and “stress” indicator |

Utility and indirect effect | Patten, B.C. [4,46,47] | Ecosystems flows serve to increase quantitative and qualitative utility of the system Indirect flows are dominating over direct effects by several orders of magnitude |

Biomass (maximum) | Straskraba, M. [48] Margalef, R [49] | Biomass as goal function Endosomatic and exosomatic causes |

**Table 2.**Historical events important to the development of thermodynamics showing the evolution from the first discoveries implicitly leading to the formulation of the first and second law, and up to our time where the connection to biology was laid out by the establishment of far from equilibrium thermodynamics.

Year(s) | Event | Ref/Source |
---|---|---|

1789–1791 | Lavoiser and Sequin discovers food combustion leading to formation of CO_{2} and H_{2}O with a parallel release of heat | after Morowitz [118] |

1824 | One of the earliest works of Sadi Carnot Betrachtungen über die Bewegende Kraft des Feuers, appears | Carnot 1824 [119] |

1865 | Clausius’ formulation of the first and second law | Clausius 1865 [120] |

1872 | Boltzmann search for the so-called H-theorem leading to Boltzmann’s formula | Boltzmann 1872 [121] |

1878 | Gibbs’ extension of the Boltzmann equation | Gibbs 1878 [122] |

1944 | Schrödinger states that living organisms are feeding on negentropy and formulates his order form order and order from disorder principles | Schrödinger 1944 [123] |

1946 | Establishment of far from equilibrium thermodynamics by Prigogine and co-workers (1) understanding of systems as dissipative structures (2) formulation of the minimum dissipation principle (3) evolution through instabilities and bifurcations | Prigogine, 1947 [70] Prigogine and Wiame, 1946 [29] Prigogine and Nicolis, 1971 [124] Prigogine and Stengers [77] Glansdorff and Prigogine, 1971 [125] Nicolis and Prigogine, 1977 [74] |

1867 | Maxwell’s demon violating the second law | Leff and Rex, 1990 [126] |

1967 | Brillouin, closer connection to information theory | Brillouin 1960 [127] |

**Table 3.**Important milestones in the application of thermodynamic principles to biological and ecological systems.

Year(s) | Event | Main Ref/Source |
---|---|---|

1922, 1925 | Lotka proposes that living organisms compete for energy | after Morowitz [118] |

1944 | Schrödinger’s states that living organisms are feeding on negentropy and formulates his order form order and order from disorder principles | Schrödinger [123] |

1976 | Exergy proposed as important factor | Jørgensen and Mejer, 1981 [38] Mejer and Jørgensen, 1979 [37] |

1979 | Exergy relates to buffer capacity | Jørgensen and Mejer, 1981 [38] |

1984 | Exergy degradation | Kay, 1984, 1991 [173,222] Kay and Schneider, 1992, [223] Schneider, 1988, [224] Schneider and Kay, 1994a,b,c [15,39,225,226] |

1987, 1989 | Entropy analysis of lake ecosystems | Aoki [35,227] |

1990–1992 | changes in ecosystems are generally accompanied by increases in exergy (storage) | Nielsen, 1992 [190] Jørgensen, 1992 [228] |

1992 | exergy storage used as goal function | Jørgensen, 1992, 1997 [229] Nielsen, 1992 [230] |

exergy relates to: intermediate disturbance hypothesis chaos ascendency the exergy “cushion” | Jørgensen and Padisak, [231] Jørgensen, [228] Nielsen and Ulanowicz [232] Reynolds [233] | |

1995 | New exergy index and specific exergy proposed based on (1) informational content of genome and (2) reference at detritus level | Jørgensen et al. [234] Bendoricchio and Jørgensen [235] |

1997 | Specific exergy covers other perspectives than the other exergy | Marques et al. [236,237] Xu [238,239] |

1997 | emergy/exergy ratios | Bastianoni and Marchettini, [58] |

**Table 4.**Showing various types of hierarchies organised according to increasing exergy. Simple components are put together constituting more and more complex structures: (a) a cathedral is complex construction eventually composed of bricks of clay, (b) organic molecules are forming cells, forming organs, forming organisms, which eventually are put together in the ecosystems, and eventually constituting the biosphere, (c) likewise the ecological food chain may be viewed as a hierarchy of increasingly complex organisms representing a higher and higher level of exergy.

(a) Architecture | (b) Biological | (c) Ecological |
---|---|---|

castle, cathedral | biosphere | top carnivore |

manor, mansion | ecosystem | carnivore |

house | societies | herbivore |

stable of bricks | populations | primary producers |

pile of bricks | organisms | bacteria |

bricks | organs | nutrients |

clay | cells | |

molecules | cell organelles | |

proteins, enzymes | ||

amino acids | ||

organic molecules | ||

inorganic molecules | ||

atoms |

Organism | Number of Information Genes | Weighting Factor |
---|---|---|

Detritus | 0 | 1 |

Minimal Cell | 470 | 2.3 |

Bacteria | 600 | 2.7 |

Algae | 850 | 3.3 |

Yeast | 2000 | 6 |

Fungi | 3000 | 10 |

Sponges | 9000 | 26 |

Plants, trees | 10,000–30,000 | 30–90 |

Worms | 10,000–100,000 | 30–300 |

Insects | 10,000–15,000 | 30–45 |

Zooplankton | 10,000–50,000 | 30–150 |

Crustaceans | 100,000 | 300 |

Fish | 100,000–120,000 | 300–350 |

Birds | 120,000 | 350 |

Amphibians | 120,000 | 350 |

Reptiles | 120,000 | 350 |

Mammals | 140,000 | 400 |

Humans | 250,000 | 700 |

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**MDPI and ACS Style**

Nielsen, S.N.; Müller, F.; Marques, J.C.; Bastianoni, S.; Jørgensen, S.E.
Thermodynamics in Ecology—An Introductory Review. *Entropy* **2020**, *22*, 820.
https://doi.org/10.3390/e22080820

**AMA Style**

Nielsen SN, Müller F, Marques JC, Bastianoni S, Jørgensen SE.
Thermodynamics in Ecology—An Introductory Review. *Entropy*. 2020; 22(8):820.
https://doi.org/10.3390/e22080820

**Chicago/Turabian Style**

Nielsen, Søren Nors, Felix Müller, Joao Carlos Marques, Simone Bastianoni, and Sven Erik Jørgensen.
2020. "Thermodynamics in Ecology—An Introductory Review" *Entropy* 22, no. 8: 820.
https://doi.org/10.3390/e22080820