Abstract
The concept of hierarchy is central to thermodynamics. Energy processes can be evaluated in terms of entropy content and the higher the entropy the lower they are positioned in the hierarchy of irreversibility. Hence, a Joule of heat at 500 K has a higher quality that the same amount of heat at 400 K. Introducing irreversibility into the Carnot machinery—the intellectual device by which we have historically developed the concept of efficiency, leads to the concept of maximum power output at suboptimal efficiency level. Introducing irreversibility—the hierarchal criterion for thermodynamics, means that time becomes a binding variable in thermal machines. Interestingly and perhaps not surprisingly, hierarchy is also a key concept of complexity. Along the line of an increasing hierarchical complexity, economic progress and evolution have been rewarding larger organizations or organisms throughout sentient or accidental selection. From microbes to whales, from villages to nations, from family firms to international corporations, the scaling up of the system has been achieved at the expenses of a growing complexity and hierarchy. To sustain the increasing complexity, processes have been increasing their power capacity thorough evolution and economic history. Is this intriguing parallel important to understand the fate of renewable energy? In this chapter I will try to expand upon the ideas of hierarchical scaling and power maximization to the problem of governing RES, with insights from finite-time thermodynamics, algometric scaling and complex science.
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Notes
- 1.
After Lotka, Odum and Pinkerton, in 1955, formalized for the first time this concept by proposing the optimal effcicieny at maximum power output (Odum and Pinkerton 1955).
- 2.
Interestingly, this principle, the strong coupling of antithetical forces, is common to the Hatwood machine Odum and Pinkerton used to introduce the maximum power principle in 1955 by means of a purely mechanical device (Odum and Pinkerton 1955).
- 3.
In the case of CA machinery, the two coupled forces are the heat injection and rejection. Another example of heat engine operating in a regime of strong coupling is a couple of thermoelectric generators (Apertet et al. 2012).
- 4.
To optimize the power in a thermal machine we can either increment the speed at which the heat is transferred to the working fluid from the hot reservoir (the combustion) or from the working fluid to the cold reservoir (the environment). A very intuitive example is that of cars: when we introduce a turbocharger, we increase the heat transfer speed (the phase of heat addiction at constant volume of the cylinder) by increasing the pressure at the same volume ratio (the piston’s size) and when we are introducing a cooling system, like a water or air cooling device, we are increasing the heat rejection by diminishing the temperature of the machine.
- 5.
It should be noted that we are hereby referring to a broader concept of “strategy” that concerns not only the operational conditions of thermal machines but also their design. Indeed a car running at the speed of a bicycle would be much more energy-efficient, but a car is conceived to run at one order of magnitude faster.
- 6.
Theoretical efficiency for plants is calculated comparing the energy carried by the photons with the energy converted in ATP by the photosynthesizer apparatus (the light absorption by pigments in disk-like thylakoid membranes inside chloroplasts in specialized leaf cells). Real efficiency compares the solar energy hitting the surface with the growth rate of the energy (calories) embodied in the phytomass, thus considering any energy loss, from plant’s respiration to inefficiency in the related cycles (Calvin cycle, etc.). For an extensive description see the Chapter dedicated to Photosynthesis in Smil (2008).
- 7.
“Actual short-term increments of new phytomass are at best 50% or, more likely, just 33% of these rates. The top seasonal or annual additions are between 20 and 25% of the ideal rates, and long-term, large-scale averages are merely 10% and all the way down to just 2% of the best hypothetical performance. The two main reasons for these disparities are the respiration costs and the inevitable losses that go with rapid rates of photosynthetic reactions. In order to conserve as much light as possible during the limited hours of intensive insolation, the rates must be quite fast, but this rapidity results in two kinds of considerable inefficiencies. Unless the plant’s enzymes can keep up with the radiation flux coming into the excited pigments, the absorbed energy will be reradiated as heat. Utilization must be immediate because the chlorophyll molecules cannot store sunlight. Only at very low light intensities, when radiation would be the only factor limiting the rate of the terrestrial photosynthesis, is there such a perfect match” (Smil 2008).
- 8.
“Quarter-power scaling laws are perhaps as universal and as uniquely biological as the biochemical pathways of metabolism, the structure and function of the genetic code, and the process of natural selection. The vast majority of organisms exhibit scaling exponents very close to 3/4 for metabolic rate and to 1/4 for internal times and distances. These are the maximal and minimal values, respectively, for the effective surface area and linear dimensions for a volume-filling fractal-like network. On the one hand, this is testimony to the power of natural selection, which has exploited variations on this fractal theme to produce the incredible variety of biological form and function. On the other hand, it is testimony to the severe geometric and physical constraints on metabolic processes, which have dictated that all of these organisms obey a common set of quarter-power scaling laws. Fractal geometry has literally given life an added dimension” (West et al. 1999).
- 9.
We tend to think of hierarchy as a designed process, the result of a sentient subject. How can be hierarchy the outcome of evolution and the result of a spontaneous process? The interesting topic of hierarchy genealogy goes beyond the scope of the present analysis, it is so complex and vast that would probably require a chapter for its own. It is the opinion of the author that an investigation on the process of hierarchy creation should expand upon the concept of symmetry breaking. Geoffrey West himself hinted to the fact that the hierarchical branching in elementary particles derives from a symmetry breaking (West 2006). The first who seemingly first envisaged the nexus between hierarchy and symmetry was Gregory Bateson, who suggested that the information for symmetry breaking may be embodied in physical or chemical gradients (Bateson 1972). The etiological bond between symmetry breaking and spatial gradients has been central to a former paper by Ruzzenenti and Basosi titled Complexity change and space symmetry rupture (Ruzzenenti and Basosi 2009).
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Ruzzenenti, F. (2017). Hierarchies, Power and the Problem of Governing Complex Systems. In: Labanca, N. (eds) Complex Systems and Social Practices in Energy Transitions. Green Energy and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-33753-1_5
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