92 – Entropy, money, investment and debt

This post is a follow-up to posts 89 and 90, in which I have shown that the state of an economy can be compared to the state of a fluid defined by its pressure P and temperature T. In post 49, I applied the concept of « temperature » to the economy. In my lecture of March 12, 2015 (post 75), I showed that the economic equivalent of the pressure P is a Gibbs potential that I called the « economic potential » of the production.

P and T are intensive variables. Each of them is associated with an extensive variable called the conjugate variable. The conjugate variable of pressure is the volume V while the conjugate variable of temperature is the entropy S. In economics, the volume V corresponds to the quantity of manufactured objects, while entropy S corresponds to their monetary value. The product P.dV represents the amount of mechanical work resulting from the manufacture a product, while T.dS represents the amount of energy dissipated by its consumption.

In my conference of March 12, 2015, I have identified the product P.dV to what economists call «demand», and the product T.dS to what they call «supply». The conservation of energy implies that supply must balance demand. In my two previous posts, I have directly assimilated P and T with demand and supply. I will continue to do so, bearing in mind that P now represents the intensity of the demand and T the intensity of the supply.

In physics, the variables P, V and T characterize the state of a fluid. They are linked by a relationship called the equation of state. For a so-called « perfect » gas, this relation is simply PV = RT, where R is the gas constant. For a real fluid, it is fairly well represented by the van der Waals equation. It is the equation of a surface of the third degree, part of which must be replaced by straight isotherms at the « condensation temperature » (see post 89).

The equation of state of a fluid expresses its volume as a function of its temperature and its pressure. The volume is the conjugate variable of the pressure. One might as well have chosen the conjugate variable of the temperature which is the entropy. The reason for this choice is that it is easier to measure changes of volume rather than changes of entropy, because measuring the latter require a calorimeter. Calorimetric measurements show that the entropy of a fluid can be represented by a point on a surface quite similar to the van der Waals surface. In particular, it includes the same condensation zone within which the fluid appears under two different phases.

To facilitate my readers’ comprehension, I made a plaster model of this surface, which is pictured below in two different diagrams. On the first, the horizontal coordinate axes represent the pressure P and the temperature T of a fluid. The vertical coordinate axis represents either the volume V or the entropy S. This surface may be usefully compared to the portion of the surface which is near the critical point as described in post 89.

In the second diagram, the horizontal coordinate axes represent the potential P of the production (marked «demand») and the temperature T of the economy (marked «supply»). The vertical coordinate axis (marked «production») represents either the volume V of production or its monetary value M. It is important to realize that a point on this surface represents the state of the economy for a given production. Some products may be in the stagflation phase while others are still in the expansion phase. The general state of the economy is then a weighted average of all of the states of production.

One can see on this model that the monetary value M of production grows throughout the economic cycle up to some point above the Seneca cliff, at which it starts to decrease before falling abruptly along the cliff. As we have seen (post 87), the decrease begins when the state of production crosses the critical isotherm. From there, capital income no longer offsets expenses, and capital decreases. Failure can occur as soon as the state of the economy reaches the edge of the Seneca cliff.

The analogy with fluids suggests that one can observe the analog of a delayed condensation. It is indeed an abrupt phase transition and these require the presence of condensation nuclei. As a fluid can stay for a while in a supercooled state, an economy can remain in state of debt, as long as the creditors do not request their due. Only when they realize they will not be paid, chain bankruptcies occur forming a cascade of events typical of self-organizing systems (post 18).

In the same way that a fluid condenses, a company which collapses must reorganize itself. New structures are formed on a small scale within which collaborations are established. This implies a reduction of entropy. In a heat engine, this phase corresponds to the evacuation of burnt gas. This is the phase during which a steam engine returns to the cold source part of the heat it has received. It gives off an amount of entropy ΔS. For a fluid which condenses, the product T.ΔS represents the latent heat of condensation. It is the heat which is released by the condensation of the fluid.

In a society, evacuated entropy is measured in monetary terms. Since cash flows are of opposite sign to entropy flows, an evacuation of entropy represents the investment of a new capital. It is for example the capital necessary to develop new energy resources during the so-called energy transition. This capital for investment plays the role of the latent heat of condensation. Its amount often adds up to the outstanding debt of the previous organization. It makes transition phases very painful to go through: these are periods of crises. In a future post, I will describe in more detail the different phases of the economy.

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