Thermodynamics and ecology

doi:10.1016/S0304-3800(00)00301-X

Ecological Modelling

Volume 132, Issues 1–2, 30 July 2000, Pages 11-22

https://doi.org/10.1016/S0304-3800(00)00301-X Get rights and content

Abstract

How to apply thermodynamic methods and concepts to ecology, how to describe the ecosystem's behaviour in terms of physics (and particularly, thermodynamics), what kind of physical criteria can be used for estimation of anthropogenic impact on ecosystems? — I try to answer these questions in this manuscript. From the viewpoint of thermodynamics, any ecosystem is an open system far from thermodynamic equilibrium, in which entropy production is balanced by the outflow of entropy to the environment. I suggest the ‘entropy pump’ hypothesis: the climatic, hydrological, soil and other environmental conditions are organised in such a way that only a natural ecosystem which is specific for these conditions can be in the dynamic equilibrium (steady-state). In the framework of this hypothesis I can calculate the entropy production for the ecosystem under anthropogenic stress. This approach was applied to the analysis of crop production in Hungary in the 1980s. Considering systems far from thermodynamic equilibrium we can prove that the so-called exergy is a functional of a dissipative function, which is undertaken along the trajectory from a thermodynamic equilibrium to a dynamic one. It was shown there is a close connection between the measure of additional information (Kullback's measure) and exergy.

Introduction

Quoting from table-talks in Moscow:

Thermodynamics is full of highly scientific and charming terms and concepts, giving an impression of philosophical and scientific profundity. Entropy, thermal death of the Universe, ergodicity, statistical ensemble — all these words sound very impressive posed in any order. But, placed in the appropriate order, they can help us to find the solution of urgent practical problems. The problem is how to find this order…

In 1948 John von Neumann said:

… nobody knows what entropy is in reality, that is why in the debate you will always have an advantage

Many studies are known which attempt to apply (directly or indirectly) thermodynamic concepts and methods in theoretical and mathematical ecology for the macroscopic description of biological communities and ecosystems. Such attempts can be divided into two classes.

The first class includes the direct transfer of such fundamental concepts as entropy, the First and Second Laws of Thermodynamics, Prigogine's theorem, etc., into ecology. The literature on this subject is enormous: recent publications are Weber et al. (1988), Jørgensen (1992), Schneider and Kay (1994).

The second class includes some attempts to use the methods of thermodynamics, such as Gibbs statistical method. Khinchin (1943) has proposed a very elegant scheme for the construction of formal statistical mechanics. This scheme could be applied to a wide class of dynamical systems, in particular, to Volterra's ‘prey-predator’ system (Kerner, 1957, Kerner, 1959, Alexeev, 1976). Unfortunately, none of these results can be interpreted satisfactorily from the ecological point of view (Svirezhev, 1976).

Strictly speaking, there are no principal prohibitions to applying thermodynamic concepts to such physical-chemical systems as ecological ones. The problem is the following: there is no direct homeomorphism between the models (in a broad sense) in thermodynamics and the models in ecology. For example, the model of ideal gas (the basic model of thermodynamics) cannot be applied directly to a population or, moreover, to a biological community. The macroscopic state of the ideal gas is an additive function of the microscopic states of molecules. The stable structure of a biological community is the consequence of interactions between populations rather than the function of characteristics of individual species, etc. It is appropriate to mention the well-known ecological paradox: the diversity of a community is maximal when the distribution of species is uniform, i.e., when there are no abundant and rare species, and no structure.

But in spite of this, I look at the problem of the application of thermodynamic ideas to ecology with optimism. I think that if we could manage to formulate the thermodynamic-ecological model correctly, and if we were able to formulate correctly the concept of the thermodynamic system in relation to ecosystems, the use of these formulations in ecology would be very fruitful.

Section snippets

The physical approach: direct calculation of the entropy and the ‘entropy pump’ hypothesis

From the viewpoint of thermodynamics, any ecosystem is an open thermodynamic system. The climax of the ecosystem corresponds to a dynamic equilibrium (steady-state), when the entropy production inside a system is balanced by the entropy flow from the system to its environment. This work is being done by the ‘entropy pump’. What does mean this?

Let us consider one unit (hectare, m², etc.) of the Earth's surface, which is occupied by a natural ecosystem (meadow, steppe, forest, etc.) maintained in

Case study: the Hungarian agricultural system

If the annual total (gross) agro-ecosystem production is equal to P₁, the net production is equal to (1−r)P₁ where r is the respiration coefficient, and the term rP₁ then describes the respiration losses. The kth fraction of the net production is being extracted from the system with the yield, so that the crop yield is equal to $y=k(1−r)P_{1} .$

The remaining fraction $(1−k)(1−r)P_{1}$ is transferred to the litter and soil. If we accept the stationary hypothesis then we must assume that the corresponding

Systems far from thermodynamic equilibrium

Before introducing some special concepts such as exergy, etc., we must remember that all these concepts consider the ecosystem as a system far from thermodynamic equilibrium. The ‘basic’ variable for this theory is the rate of entropy production, or the rate of energy dissipation, the so-called the dissipative function (β). Immediately a series of questions arises, dealing with the behaviour of the dissipative function β.

1.
How can we calculate the dissipative function β for the system far from

Exergy and entropy: exergy maximum principle

Let us suppose that the right-hand sides of equations inEq. (16) depend on some parameters $α_{1},..., α_{m}$ , so that $d C_{i} d t =f_{i} (C_{1},...,C_{n}; α_{1},..., α_{m}), i=1,..., n.$

The vector of parameters α describes a state of the environment. It is obvious that the equilibrium C^* depends on α. Let us consider the following ‘Gedankenexperiment’:

1.
Let the current state of environment be described by the vector α¹, then C^*=C^*(α₁).
2.
We change the environment from the state α¹ to the state α² very quickly in comparison with the own

Exergy and information

Introducing the new variables $p_{i} =C_{i} / ∑ i=1 n C_{i}, ∑ i=1 n C_{i} =A,$ where A is the total amount of matter in the system, we can rewrite formula Eq. (20) in the form $Ex/RT=A ∑ i=1 n p_{i} ln p_{i} p_{i}^{0} + A ln A A_{0} −(A−A_{0}) .$

The vector p={p₁,…, p_n} describes the structure of the system, i.e. p_i are intensive variables. The value A is an extensive variable. The expression $K= ∑ i=1 n p_{i} ln(p_{i} /p_{i}^{0})≥0$ is so-called Kullback's measure, which is very popular regarding information measure. Let us consider what the exact meaning of the Kullback

Conclusion

In my presentation I tried to demonstrate how to apply the concepts and methods of classical (and non-classical) thermodynamics to ecological problems. Ecosystems are systems far from the thermodynamic equilibrium and when we try to calculate the entropy by a direct way we immediately get into such difficulties that the solution of the problem becomes very ‘problematic’. However, by using the ‘entropy pump’ hypothesis we can calculate the entropy production for ecosystems under anthropogenic

Acknowledgements

I am grateful to Professor Istvan Lang, Former General Secretary of the Hungarian Academy of Sciences, for his invaluable help with my ‘thermodynamics and agriculture’ work. I am indebted also to Professor S.-E. Jørgensen for his helpful comments and criticism and to Alison Schlums for her careful linguistic editing of my manuscript.

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(1974)
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There are more references available in the full text version of this article.

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^☆: Presented at the 9th ISEM Conference held in Beijing, PR China, 11–15 August, 1995

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Thermodynamics and ecology☆

Abstract

Introduction

Section snippets

The physical approach: direct calculation of the entropy and the ‘entropy pump’ hypothesis

Case study: the Hungarian agricultural system

Systems far from thermodynamic equilibrium

Exergy and entropy: exergy maximum principle

Exergy and information

Conclusion

Acknowledgements

Futures

Biophysics of living communities

Uspekhi fisicheskikh nauk

Energy Efficiency of Fertilisers in Agroecosystems

Soil Geography

Integration of Ecosystem Theories: A Pattern

Statistical mechanics of interacting biological species

Bull. Math. Biophys.

Futher considerations on the statistical mechanics of biological associations

Bull. Math. Biophys.

Mathematical Foundations of Statistical Mechanics