Thermodynamics and ecology☆
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
The remaining fraction 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 , so that
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 variableswhere A is the total amount of matter in the system, we can rewrite formula Eq. (20) in the form
The vector p={p1,…, pn} describes the structure of the system, i.e. pi are intensive variables. The value A is an extensive variable. The expressionis 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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Presented at the 9th ISEM Conference held in Beijing, PR China, 11–15 August, 1995