The Second Law of Thermodynamics interpreted for open systems

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Let us first expand on the conclusions that we have already made to give more detail on the difference between isolated and open systems and thereby understand better the application of the Second Law to open systems (J0rgensen et al., 1999).

If ecosystems were isolated, no energy or matter could be exchanged across their boundaries. The systems would spontaneously degrade their initially contained work capacity, i.e. exergy (for details see Chapter 5) and increase their entropy, corresponding to a loss of order and organisation, and increase in the randomness of their constituents and microscopic states. This dissipation process would cease at equilibrium, where no further motion or change would be possible. The physical manifestation would ultimately be a meltdown to the proverbial "inorganic soup" containing degradation products dispersed equally through the entire volume of the system. All gradients of all kinds would be eliminated, and the system would be frozen in time in a stable, fixed configuration. The high-energy chemical compounds of biological systems, faced suddenly with isolation, would decompose spontaneously to compounds with high entropy contents. The process would be progressive, to higher and higher entropy, and would, by the presence of oxygen, end with a mixture of inorganic residues—carbon dioxide and water, nitrates, phosphates, sulphates, etc. These simpler compounds could never be reconfigured into the complex molecules necessary to carry on life processes without the input of new low-entropy energy to be employed in biosynthesis. An isolated ecosystem could therefore, in the best case, sustain life for only a limited period of time, less than that required from the onset of isolation to reach thermodynamic equilibrium. This local situation is comparable to the "thermal death" of the Universe, seen by physicists of a century ago as the ultimate outcome of the Second Law of Thermodynamics. Thus, thermodynamic equilibrium is the global attractor for all physical processes isolated from their surroundings. Having reached it, no further changes are possible. In this "frozen" state, even time would have no meaning as its passage could not be verified by reference to any changes. Observations of properties could not be made, only inferred, because observation requires some kind of exchanges between the system and an observer. There would be no internal processes, because no gradients would exist to enable them. There would only be uninterrupted and uninterruptable stillness and sameness which would never change. The system would be completely static at the thermodynamic equilibrium. Thus, in a peculiar way, isolated systems can only be pure abstractions in reality, submitting neither to time passage, change, nor actual observation. They are the first "black holes" of physics, and the antithesis of our systems plus their environments which are the core model for systems ecology. No ecosystem could ever exist and be known to us as an isolated system.

The change in entropy for an open system, dS, consists of an external, exogenous contribution from the environment, deS = (gjn — q^dí, where qfn and qSut are inflows and outflows of entropy, and an internal, endogenous contribution due to system state, diS, which should always be positive by the Second Law (Prigogine, 1955). Prigogine uses the concept of entropy and the Second Law of Thermodynamics far from thermodynamic equilibrium, which is outside the framework of classic thermodynamics, but he uses the concepts only locally.

There are three possibilities for the entropy balance:

dt dt dt

The system loses order in the first case. Gaining order (case 2), is only possible if de- . d— . 0 dt dt '

This means that, if order is to be created in a system (dS/dt < 0), deS/dt must be negative, and therefore qSn < q^.

Creation of order in a system must be associated with a greater flux of entropy out of the system than into the system. This implies that the system must be open or at least non-isolated.

Case 3, Eq. (2.3), corresponds to a stationary situation, for which Ebeling et al. (1990) use the following two equations for the energy (U) balance and the entropy (S) balance:

Usually, the thermodynamic processes are isotherm and isobar. This implies that we can interpret the third case (Eqs. (2.3) and (2.5), and (2.6)) by use of the Gibbs free energy:

dt dt

It means that a "status quo" situation for an ecosystem requires input of free energy to compensate for the loss of free energy and corresponding formation of heat due to maintenance processes, i.e. respiration and evapotranspiration. If the system is not receiving a sufficient amount of free energy, the entropy will increase. If the entropy of the system continues to increase, the system will approach thermodynamic equilibrium—the system will die. This is in accordance with Ostwald (1931): life without the input of free energy is not possible.

The entropy produced by the life processes can be exported by three processes: (1) transfer of heat to the environment, (2) exchange of material with the environment, and (3) biochemical processes in the system. The first process (heat transfer) is of particular importance.

An energy flow of about 1017 W by solar radiation ensures the maintenance of life on Earth. The surface temperature of the Sun is 5800 K and of the Earth on average about 280 K. This implies that the following export of entropy per unit of time takes place from Earth to the open space:

1017 W(1 /5800 K - 1 /280 K) < 4 X 1014 W/K (2.8)

corresponding to 1 W/m2 K.

Ecosystems can maintain a certain concentration of low-entropy compounds against the second-law dissipation gradient because they are not isolated. Ecosystems receive a continuous supply of free energy or negentropy (potential entropy, not yet released (see Schrodinger, 1944)) from outside to compensate for the positive entropy produced internally as a consequence of the Second Law of Thermodynamics (diS > 0). On Earth, solar radiation is the main source of this input of free energy, negentropy or low-entropy energy. The incoming energy has low entropy, while the outgoing energy has higher entropy.

All ordered structures require low entropy for maintenance and, therefore, for a system to maintain structure or increase its internal order, it must receive input of low-entropy energy from external sources. Structure, in this context, is a spatial or temporal order, describable in terms of information theory (see Chapter 4). Prigogine uses the term dissipative structure to denote self-organising systems, thereby indicating that such systems dissipate energy (produce entropy) for the maintenance of their organisation (order). The following conclusions are appropriate:

All systems, because they are subject to the Second Law of Thermodynamics, are inherently dissipative structures. To offset the dissipative processes, they require inputs of low-entropy energy to maintain or produce more internal organised structure, measurable in terms of information content. Thus, all real systems must be open or, at least, non-isolated.

Ecosystems, in common with all real systems, have, as previously noted, a global attractor state, thermodynamic equilibrium. Through their openness, they avoid reaching this state by importing low entropy, or matter carrying information from their surroundings. This anabolism combats and compensates for the catabolic deterioration of structure; the two processes operate against one another. Note that the equilibrium "attractor" represents a resting or refractory state, one that is passively devolved if system openness or non-isolation is compromised (J0rgensen et al., 1999). The term is also commonly used to express the situation when a system is actively pushed or "forced" towards a steady state. Though widespread, we do not subscribe to this usage and make a distinction between steady states and equilibriums for two reasons:

1. The state-space system theory we outlined in the "conservation" chapter (Patten et al., 1997) precludes anything in system dynamics but a unique input-state-output relationship. Therefore, given an initial state, state-space theory asserts that there exists one and only one sequence of inputs that will put an open system in a given state at a specified final time. For this terminal state to be an "attractor", many input sequences would have to be able to place the system in it, and from many initial states—the attractor would be hard to avoid.

2. As observed above, a steady state is a forced (non-zero input) condition; there is nothing "attractive" about it. Without a proper forcing function, it will never be reached or maintained. A steady state that is constant may appear in equilibrium, but it is really far from equilibrium and maintained by a steady input of energy or matter. We regard equilibrium as a zero-input condition. What are often recognised as local attractors in mathematical models really have no counterparts in nature. Steady states are forced conditions, not to be confused with unforced equilibriums, which represent states to which systems settle when they are devoid of inputs. The only true natural attractor in reality, and it is global, is the unforced thermodynamic equilibrium. See Patten et al. (1997) for further clarification of the basis for these distinctions.

The overall results of these processes are consistent with the energy charge-discharge cycles introduced and discussed in detail in Patten et al. (1997). The consequences of the openness may be stated in three different ways to emphasise the different perspectives provided by, respectively, energy, entropy, and thermodynamic equilibrium (J0rgensen et al., 1999):

1. Energy. Energy, mainly as solar radiation but also contained in certain inorganic substances of geochemical origin, is transferred in anabolism to high molecular weight, high energy, organic compounds (charge phase). These compounds are decomposed in catabolism along step-wise molecular pathways to release high quality energy which powers biological processes (discharge phase). This energy is degraded in the performance of work to lower quality energy in the form of heat which leaves the system, necessitating subsequent anabolic recharge. The quantity of energy is conserved, but not the energy quality (measured by its ability to do work). The energy quality is degraded by this charge-discharge cycle.

2. Entropy. A certain quantity of negentropy is embodied in solar and geochemical energy. Some of this negentropy is built in anabolic processes into the organised structure of biomolecules (charge phase). Progressive decomposition of these molecules in catabolism releases the entropy as the low-entropy energy is converted to high-entropy heat (discharge phase). The entropy reduces the overall order and organisation of the system and its environment. Thus, organised (low-entropy) states of ecosystems and their organisms can only be achieved and maintained at the expense of their respective environments by, in effect, "pumping out disorder" as high-entropy released heat.

3. Thermodynamic equilibrium. The energy of solar radiation and inorganic compounds used in photosynthesis and chemosynthesis is high quality energy far from thermodynamic equilibrium (as reflected in their exergy and negentropy contents). Systems move further from equilibrium (and their energies and negentropies increase) to the extent that this energy becomes incorporated into their organised structure (charge phase). If a far-from-equilibrium system becomes isolated, or is otherwise severed from its energy sources, then it will spontaneously decay by irreversible processes toward thermodynamic equilibrium (discharge phase). Continual input of high quality energy as a forcing function is required for a system to achieve and maintain a steady state far from equilibrium.

In each of the above three descriptions of the same input-output phenomenon associated with system non-isolation and openness, the opposition of successive charge and discharge phases can be seen as an antagonism or "combat" between anabolic and catabolic processes. The first seeks to build up structural organisation against the gradient provided by the Second Law of Thermodynamics. The second inexorably tears it down toward thermodynamic equilibrium. Far from equilibrium, energy of high quality is degraded to heat, exergy is consumed in performing work, and negative entropy is converted to positive entropy as self-organising systems are spontaneously and irreversibly drawn toward the global attractor that is thermodynamic equilibrium. Openness or non-isolation is a necessary condition for avoidance of this state, for it is only by the exchange of energy or matter across system boundaries that the far-from-equilibrium condition can be reached and sustained. This is because the total entropy is not preserved but will steadily increase for any irreversible process. An ecosystem must, therefore, to repeat the previous arguments, be able to dissipate the generated entropy as heat to its environment. Otherwise, temperature would increase without bound and life in ecosystems as we know it could not be supported.

The following conclusion pertains to the two environments of every ecosystem:

Input environments of ecosystems serve as sources of high quality energy whose high contents of free energy and low entropy raise the organisational states of matter far from equilibrium. Output environments, in contrast, are sinks for energy higher in entropy, and closer to equilibrium. Since, in the organisation of ecosystems, output environments feed back to become portions of input environments, living systems operating in the ecosphere, which is energetically non-isolated but materially nearly closed, must seek an adaptive balance between these two aspects of their environmental relations in order to sustain their continued existence.

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