The dissipative systems model

The theory of dissipative structure upon which the current discussion is based can be treated as the open systems model extended with a capability to continuously impose a revolutionary change or transformation.

The theory of dissipative structure

Pioneered by the Brussels school of thought in the 1970s (Prigogine, 1976; Nicolis and Prigogine, 1977, 1989; Prigogine and Stengers, 1984), this theory is firmly rooted in physics and chemistry. Nevertheless, it was later applied to urban spatial evolution (Allen and Sanglier, 1978, 1979a, 1979b, 1981), organisational change and transformation (Gemmill and Smith, 1985; Leifer, 1989; Macintosh and Maclean, 1999), changes in small groups and group dynamics (Smith and Gemmill, 1991), and political revolutions and change in political systems (Artigiani, 1987a, 1987b; Byeon, 1999).

Dissipative structure in physical systems

The most prominent example of dissipative structure in a physical system is convection in a liquid (Nicolis and Prigogine, 1977; Jantsch, 1980; Prigogine and Stengers, 1984). If cooking oil is heated in a shallow pan, the following macroscopic changes occur. Firstly, while the temperature of liquid is relatively uniform, heat is transmitted through the body of liquid by means of conduction in which the molecules’ heat energy (molecular vibration) is transmitted to neighbouring molecules via collision without major change of position. We can say that the system is still in a thermodynamic equilibrium. Next, as the pan is heated further, the temperature gradient between the upper and lower portion of the oil in the pan becomes more pronounced and thermal non-equilibrium increases. At a certain temperature gradient, convection starts and heat is then transferred by the bulk movement of molecules. Evidently, however, the surrounding environment at first suppresses the smaller convection streams, but beyond a certain temperature gradient, the fluctuations are reinforced rather than suppressed. The system moves into a dynamic regime, switching from conduction to convection, and a new macroscopic order called ‘Benard cells’ (i.e. a pattern of regular hexagonal cells that appear on the surface of liquid) emerges, caused by a macroscopic fluctuation and stabilised by an exchange of energy with the environment. Such a structure is called a hydrodynamic dissipative structure, and is a version of spatial structure (Haken, 1980).

Order in a non-equilibrium state

As mentioned earlier, open systems make an effort to avoid a transition into thermodynamic equilibrium by a continuous exchange of materials and energy with the environment. By doing this, a negative entropy condition can be maintained. It has been understood for a long time that entropy is a quantification of randomness, uncertainty, and disorganisation, and negative entropy therefore corresponds to (relative) order, certainty, and organisation (Bertalanffy, 1973; Kramer and De Smith, 1977; Nicolis and Prigogine, 1977; Prigogine and Stengers, 1984; Miller, 1978; Van Gigch, 1978, 1991; Flood and Carson, 1993). However, the mechanics underlying this idea had not been clear until it was explained in the work of Nicolis and Prigogine (1977), Prigogine and Stengers (1984), and Jantsch (1980) in the theory of dissipative structure and order that exists in the non-equilibrium condition.

According to the theory of dissipative structure, an open system has a capability to continuously import free energy from the environment and, at the same time, export entropy. As a consequence, the entropy of an open system can either be maintained at the same level or decreased (negative entropy), unlike the entropy of an isolated system (i.e. one that is completely sealed off from its environment), which tends to increase toward a maximum at thermodynamic equilibrium. This phenomenon can be represented in quantitative terms as follows (Nicolis and Prigogine, 1977; Jantsch, 1980; Prigogine and Stengers, 1984). According to the second law of thermodynamics, in any open system, change in entropy dS in a certain time interval consists of entropy production due to an irreversible process in the system (an internal component) diS and entropy flow due to exchange with the environment (an external component) deS. Thus, a change in entropy in a certain time interval can be represented as dS = deS + diS (where diS > 0). However, unlike diS, the external component (deS) can be either positive or negative. Therefore, if deS is negative and as numerically large as, or larger than, diS, the total entropy may either be stationary (dS = 0) or decrease (dS < 0). In the former case, we can say that the internal production of entropy and entropy exported to the environment are in balance. An open system in a dissipative structure sense can be viewed as shown in Figure 11.4, “An open system’s entropy production and dissipation.”.

Figure 11.4. An open system’s entropy production and dissipation.

An open system’s entropy production and dissipation.

It can be concluded that order in an open system can be maintained only in a non-equilibrium condition. In other words, an open system needs to maintain an exchange of energy and resources with the environment in order to be able to continuously renew itself.

Entropy and sustainability of dissipative systems

The internal structure and development of dissipative systems, as well as the process by which they come into existence, evolve, and expire, are governed by the transfer of energy from the environment. Unlike isolated systems (or closed systems in a broader sense), which are always on the path to thermal equilibrium, dissipative systems have a potential to offset the increasing entropic trend by consuming energy and using it to export entropy to their environment, thus creating negative entropy or negentropy, which prevents the system from moving toward an equilibrium state. A negentropic process is, therefore, the foundation for growth and evolution in thermodynamic systems.

For dissipative systems to sustain their growth, they must not only increase their negentropic potential, but they must also eliminate the positive entropy that naturally accumulates over time as systems are trying to sustain themselves. The build up of the system’s internal complexity as it grows is always accompanied by the production of positive entropy (diS > 0), which must be dissipated out of the system as waste or low-grade energy. Otherwise, the accumulation of positive entropy in the system will eventually bring it to thermodynamic equilibrium, a state in which the system cannot maintain its order and organisation (Harvey and Reed, 1997).