# Towards a Thermodynamic Theory for Ecological Systems

**By**

- S.E. Jorgensen, DFH, Miljokemi, Copenhagen, Denmark
- Y.M. Svirezhev, Potsdam Institute for Climate Impact Research, Germany

The book presents a consistent and complete ecosystem theory based on thermodynamic concepts. The first chapters are devoted to an interpretation of the first and second law of thermodynamics in ecosystem context. Then Prigogine's use of far from equilibrium thermodynamic is used on ecosystems to explain their reactions to perturbations. The introduction of the concept exergy makes it possible to give a more profound and comprehensive explanation of the ecosystem's reactions and growth-patterns. A tentative fourth law of thermodynamic is formulated and applied to facilitate these explanations. The trophic chain, the global energy and radiation balance and pattern and the reactions of ecological networks are all explained by the use of exergy. Finally, it is discussed how the presented theory can be applied more widely to explain ecological observations and rules, to assess ecosystem health and to develop ecological models.

View full description### Book information

- Published: July 2004
- Imprint: PERGAMON
- ISBN: 978-0-08-044167-2

### Reviews

it was a pleasure to read it and appreciate new concepts and ideas. ...that publishing houses are giving enough space to bringing multidisciplinary areas to the attention of readers, excellent example being the book reviewed.

JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY, 2005

The post-scriptum is an excellent summary of the laws of the ecosystem theory. The book is highly recommendable to all scientists and young researchers interested in the new scientific paradigm of evolutionary thermodynamics.

E. Tiezzi, Ecological Modelling, 2005

### Table of Contents

Preface.**1. Thermodynamics as a method: A problem of statistical description.**1.1 Literary introduction. 1.2 Ontic openness. 1.3 The scope of this volume.

**2. The laws of classical thermodynamics and their application to ecology.**2.1 Introduction. 2.2 Matter and energy in mechanics and thermodynamics. Energy conservation as the first law of thermodynamics. Fundamental Gibbs Equation. 2.3 Entropy and the second law of thermodynamics: Nernst's theorem. 2.4 Maximal work which the system can perform on its environment. Characteristic functions or thermodynamic potentials. 2.5 Chemical equilibrium, chemical affinity and standard energies of biochemical reactions. Function of dissipation. 2.6 Illustrations of thermodynamics in ecology. 2.7 Ecosystem as a biochemical reactor. 2.8 Summary of the important ecological issues.

**3. Second and third law of thermodynamics in open systems.**3.1 Open systems and their energy balance. 3.2 The second law of thermodynamics interpreted for open systems. 3.3 Prigogine's theorem and the evolutionary criterion by Glansdorff-Prigogine. 3.4 The third law of thermodynamics applied on open systems. 3.5 Thermodynamics of living organisms. 3.6 Quantification of openness and allometric principles. 3.7 The temperature range needed for life processes. 3.8 Natural conditions for life.

**4. Entropy, probability and information.**4.1 Entropy and probability. 4.2 Entropy and information. 4.3 The system as a text and its information entropy. 4.4 Diversity of biological communities. 4.5 Simple statistical models of biological communities. 4.6 Information analysis of the global vegetation pattern. 4.7 Diversity of the biosphere. 4.8 Information and evolutionary paradigm: Selection of information. 4.9 Genetic information contained in an organism: Hierarchy of information and its redundancy. 4.10 Summary of the important ecological issues.

**5. Work, exergy and information.**5.1 The work done by a system imbedded into an environment. 5.2 What is exergy? Different interpretations of the exergy concept. 5.3 Thermodynamic machines. 5.4 Exergy far from thermodynamic equilibrium. 5.5 Exergy and information. 5.6 Exergy of solar radiation. 5.7 How to calculate the exergy of living organic matter? 5.8 Other methods for the exergy calculation. 5.9 Why have living systems such a high level of exergy? 5.10 Summary of the important ecological issues.

**6. Stability in mathematics, thermodynamics and ecology.**6.1 Introduction. Stability concepts in ecology and mathematics. 6.2 Stability concept in thermodynamics and thermodynamic measures of stability. 6.3 Model approach to definitions of stability: Formal definitions and interpretations. 6.4 Thermodynamics and dynamical systems. 6.5 On stability of zero equilibrium and its thermodynamic interpretation. 6.6 Stability of non-trivial equilibrium and one class of Lyapunov functions. 6.7 Lyapunov function and exergy. 6.8 One more Lyapunov function. 6.9 What kind of Lyapunov function we could construct if one or several equilibrium coordinates tends to zero. 6.10 Once more ecological example. 6.11 Problems of thermodynamic interpretation for ecological models. 6.12 Complexity versus stability. 6.13 Summary of the ecological important issues.

**7. Models of ecosystems: Thermodynamic basis and methods. I. Trophic chains.**7.1 Introduction. 7.2 General thermodynamic model of ecosystem. 7.3 Ecosystem's organisation: Trophic chains. 7.4 Dynamic equations of the trophic chain. 7.5 Prigogine-like theorems and the length of trophic chain. 7.6 The closed chains with conservation of matter. Thermodynamic cost of biogeochemical cycle. 7.7 Complex behaviour: Cycles and chaos. 7.8 What kind of exergy dynamics are when the enrichment and thermal pollution impact on the ecosystem? 7.9 Embodied energy (emergy). 7.10 Summary of the ecological important issues.

**8. Models of ecosystems: Thermodynamics basis and methods. II. Competition and trophic level.**8.1 Introduction. 8.2 Thermodynamics of a competing community. 8.3 Community trajectory as a trajectory of steepest ascent. 8.4 Extreme properties of the potential W and other potential functions. Entropy production and Prigogine-like theorems. 8.5 The system of two competing species. 8.6 Phenomenological thermodynamics of interacting populations. 8.7 Community in the random environment and variations of Malthusian parameters. 8.8 Summary of the ecological important issues.

**9. Thermodynamics of ecological networks.**9.1 Introduction. 9.2 Topology of trophic network and qualitative stability. 9.3 Dynamic models of trophic networks and compartmental schemes. 9.4 Ecosystem as a metabolic cycle. 9.5 MacArthur's diversity index, trophic diversity and ascendancy as measures of organisation. 9.6 How exergy helps to organise the ecosystem. 9.7 Some dynamic properties of trophic networks. 9.8 Stability and reactions of a bog in the temperate zone. 9.9 Summary of the ecological important issues.

**10. Thermodynamics of vegetation.**10.1 Introduction. Energetics of photosynthesis. 10.2 Thermodynamic model of a vegetation layer. Fluxes of heat, water vapour and other gases. 10.3 Energy balance of a vegetation layer and the energy efficiency coefficient. 10.4 Thermodynamic model of vegetation: Internal entropy production. 10.5 Vegetation as an active surface: The solar energy degradation and the entropy of solar energy. 10.6 Vegetation as an active surface: Exergy of solar radiation. 10.7 Simplified energy and entropy balances in the ecosystem. 10.8 Entropy overproduction as a criterion of the degradation of natural ecosystems under anthropogenic pressure. 10.9 Energy and chemical loads or how to convolute the vector data. 10.10 Summary of the ecological important issues.

**11. Thermodynamics of the biosphere.**11.1 Introduction. 11.2 Comparative analysis of the energetics of the biosphere and technosphere. 11.3 Myth of sustainable development. 11.4 Thermodynamics model of the biosphere. 1. Entropy balance. 11.5 Thermodynamics model of the biosphere. 2. Annual increment of entropy in the biosphere. 11.6 Exergy of solar radiation: global scale. 11.7 Exergy of the biosphere. 11.8 Exergy and the evolution. 11.9 Summary of the ecological important issues.

**12. Teleology and extreme principles. A tentative fourth law of thermodynamics.**12.1 Introduction. 12.2 The maximum power principle. 12.3 Hypothesis: A thermodynamic law of ecology. 12.4 Supporting evidence. 12.5 Other ecosystem theories. 12.6 Toward a consistent ecosystem theory. 12.7 Some final comments.

**13. Application of exergy as ecological indicator and goal function in ecological modelling.**13.1 Introduction. 13.2 Exergy and specific exergy as ecological indicators. 13.3 Assessment of ecosystem integrity. An example: A lake ecosystem. 13.4 Thermodynamics of controlled ecological processes and exergy. 13.5 Modelling the selection of Darwin's finches. 13.6 Exergy of the global carbon cycle: How to estimate its potentital useful work.Postscriptum.References.