Forces in thermodynamics and Economic Value Theory

In thermodynamics a branch of non-equilibrium thermodynamics, irreversible thermodynamics, emerges in the beginning of the 20^th century, based on the pioneering work of Onsager (1931a, 1931b). Before that, thermodynamics restricts itself to equilibrium situations or idealizations such as reversible processes. Irreversible thermodynamics analyzes situations beyond thermodynamic equilibrium where processes take place driven by thermodynamic forces. It turns out that the ratio of free energy,G, and temperature, T, defines thermodynamic forces, indicated by the symbol X:

) / (GT

X ' (5.7) In this equation, the symbol ߂stands for a difference. For the general case, there are many

X1 Value X₂

Transducer J1

J2

Fig. 5.2. A value transducer.

53 forces and corresponding processes. For simplicity’s sake we stick to the case of two forces driving two processes. This case stays manageable from the (mathematical) complexity point of view and shows all the fundamental features necessary for and relevant to the subject matter of this book. As said, the forces drive processes and we illustrate this using the example of a value transducer (Fig. 5.2). We adopt the EVT analogue of the thermodynamic forces to define forces in terms of differences in the ratio of economic value and cost of information.

The input side of the value transducer is an exchange flow due to a force X₁ defined in terms of economic value, its rate isJ₁. The input force is positive and the process proceeds spontaneously from the perspective of the second law as the process produces statistical entropy. We term such process downhill from the perspective of the second law. The term downhill reflects the analogy of a river flowing downhill from a mountain, i.e. in the direction we naturally expect it to flow. The output side of the value transducer involves a process that proceeds against the direction of the second law, as the force is negative. However, the flow is positive because the mechanisms inside the value transducer couple the downhill process at the input side to the uphill process at the output side. In the heat engine example, this output is the transformation of heat into work. This process of coupling of uphill to downhill processes is fundamental to the understanding of evolution. To illustrate this we further explore the relation between the second law and structures like the value transducer introduced here.

Our analysis concerns the simplest case of value transduction. It takes place in analogy to the so-called linear region of irreversible thermodynamics. The linear value transducer operates beyond equilibrium but we stay relatively close to equilibrium where linear relations between the flows and the forces prevail. In that case, the following equations describe the behavior of the transducer in Fig. 5.2: In eqns. 5.8 and 5.9 the L’s are constants not dependent on the forces, i.e. the flows are true linear combinations of the forces.

Several interesting features appear in these equations. Firstly, we need to introduce some jargon.

X1 and X₂ are the so-called conjugate forces of the input and the output flows respectively.

These forces directly drive their conjugate flows. Additionally, these forces are non-conjugate to the flows at the output and the input respectively. The forces also drive their non-conjugate flows. This so-called coupling is, as said, crucial for understanding complex real systems. As is apparent from eqns. 5.8 and 5.9, the coupling coefficient of flow 1 to force 2 equals that of the reverse coupled pair. We can visualize this so-called reciprocity if we assume coupling based on a friction mechanism. When to surfaces move relatively to each other they both experience the same friction force. Among others the present author (Roels 2010, 1983), analyzed the linear value transducer extensively. Here we avoid the mathematics of the analysis and only cite the conclusions.

As said, the heat engine is an example of coupling of a heat flow and generation of power. Power is the work per unit time and that is the quantity of interest in practice, reversible infinitely slow exchange of work has no practical meaning. Power output or input is proportional to the product of a flow and its conjugate force. An example is the hydrodynamic generation of electrical power by the coupling of uphill and downhill processes. In this case, a dam in a river flowing downhill contains a power generation plant. The water flowing through the dam drives an electrical generator and electrons move up a gradient in voltage. This process results in useful energy by the coupling of the generation of electrical power to the natural process of the water flowing

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downhill. This positive force drives electrons uphill against the gradient in voltage.

Of course, as all systems, the transducer is subject to the second law and as irreversible processes take place in the transducer, the entropy production in the combined coupled processes must exceed zero; the equality sign cannot apply, as we are not in equilibrium. This leads to conclusions about the magnitude of the coefficients in eqns. 5.8 and 5.9. The coefficients of coupling of the flows to their conjugate forces must be positive. Furthermore, there is an upper limit to the coefficient of cross coupling, the coupling of the flows to their non-conjugate force.

This upper limit defines a so-called degree of coupling that must always be smaller than one.

In the value transducer a dissipation of power takes place equal the product of the cost of information and the production of statistical entropy. This dissipation is necessarily positive because the value transducer being beyond equilibrium must show a positive entropy production due to the second law. Hence, Prigogine (1980) coined the term dissipative structures for systems like the value transducer. They escape the forces of the second law by dissipation of part of the power derived from their coupling to a positive force in their environment. The structures have lower statistical entropy than the one characteristic for thermodynamic equilibrium. A careful analysis of the linear value transducer reveals that these structures exhibit the phenomenon of so-called maintenance dissipation, i.e. they need power dissipation even if they do not produce power. If they do not have access to sufficient power to dissipate, their structures degrade and the system’s entropy increases until it reaches equilibrium.

This author (Roels (1983)) used the model of the value transducer to study so-called oxidative phosphorylation in microorganisms. Microorganisms oxidize an energy source such as sugar to carbon dioxide and water; this is equivalent to a process of low temperature burning just as the heat engine uses coal. However, it is a very intricate and clever process of burning in which energy only partly emerges as heat; a part serves to transform ADP in ATP, complex chemical substances whose naming does not have to bother us. ATP is the free energy currency of the cell.

It supplies it with free energy to grow and maintain its non-equilibrium structure. The efficiency of the generation of power in oxidative phosphorylation is of the order of 60-65%. This compares with the efficiency of the generation of electrical power in a power plant that is in the order of 50%. Roels followed the Nobel laureate Schrödinger (Schrödinger (1945)) in the view that microorganisms are dissipative structures that feed on “negentropy”, the term Schrödinger coined to indicate free energy. Furthermore, Roels identified the maintenance dissipation in the energy transducer as the known feature of maintenance energy in microorganisms. Recent work (Roels (2010)) identifies industrial corporations as examples of dissipative structures that feed on sources of economic value, such as the need for a product in the market that allows an economic transaction resulting in the capacity to do economic work. We analyze this analogy further in subsequent chapters (particularly Chapter 7).

We can use the example of microorganisms to further illustrate the feature of coupling of a thermodynamically downhill process to an uphill process against the natural direction dictated by the second law. Consider a microorganism growing on the sugar glucose (of course, it also needs sources of the other chemical elements in biomass but we can conveniently ignore this for the purpose of the discussion here). As said, part of the glucose is oxidized to result in carbon dioxide and water. Part of the energy that this combustion process releases conserves in a source of free energy, ATP. This part of the glucose drives a thermodynamically downhill process. It is the input of the value transducer of our organism. Another part of the glucose is used for building new biomass. This represents an uphill process as the free energy of the product, biomass, exceeds that of the glucose used. However, the free energy in the ATP the combustion of glucose generates drives this process. As ATP is part of a closed cycle in the organism, we can ignore it in our thermodynamic analysis and the net effect is that an uphill process, the production of biomass from glucose, is driven by a downhill process, the combustion of glucose. In fact, ATP provides the mechanism by which the downhill and uphill process couple.

55 We conclude this section by pointing out some differences between dissipative structure and equilibrium structures. Also at equilibrium, ordered structures appear. The classical example of the difference between dissipative and equilibrium structures is the distinction between a snowflake and a microorganism. Snowflakes, structures composed of ice crystals, have a beautifully ordered appearance. Snowflakes are equilibrium structures. Microorganisms, on the other hand, are marvels of order at the molecular level and need support by a constant flow of a source of energy, such as sugar. Microorganisms are dissipative structures. The same applies to a city. A city only maintains its structure and order if a continuous flow of food and energy from the environment exists. Another difference rests in the ability to generate work. Snowflakes being equilibrium structure do not dissipate and produce no work.

Dissipative structures can do work. Prigogine and his co-workers proposed dissipative structures as a model of complex organized structures such as organisms. In earlier work of this author (Roels (2010), we propose these structures as a model for the evolution of the socioeconomic system, including organizations like industrial corporations. We return to these matters in e.g. Chapter 6 discussing a systems theory of evolution and in Chapter 7 where we discuss the nature of the firm.