The second law of thermodynamics, also known as the « Carnot principle » tells us that one cannot sustainably produce mechanical energy other than by means of transformation cycles extracting heat from a hot source and giving some of it back to a cold source.

By nature, a dissipative structure continuously produces mechanical energy in order to dissipate it. This implies that it must perform transformations cycles. So in order to dissipate solar energy, the earth’s atmosphere produces cyclones and anticyclones, but also cycles such as the water cycle. Chemical elements are constantly recycled through cycles, such as carbon, nitrogen or phosphorus. Finally life itself exists only through cycles in which plants are eaten by small animals, which in turn are eaten by larger animals, whose wastes feed bacteria which produce fertilizers for plants.

Among all dissipative structures on Earth, those that dissipate the most energy are by far human societies. The science that studies how human societies dissipate energy is called economics. The first evidence of economic cycles is generally attributed to a French physician and economist, Clément Juglar, to which he attributed a period of about 8 years. In the early twentieth century, Kondratiev has pointed to longer cycles of the order of half a century.

In this blog, I myself talked about the four seasons of the economy (articles # 72 and 73), each season being of the order of a generation. This also leads to cycles having a period of about a century. In their book entitled « Secular cycles (1) » Turchin and Nefedov highlight historical cycles of even longer periods, about 400 years (see the list of these cycles the bottom of this post). For each of them, Turchin and Nefedov clearly identify four phases to which they give the following names: the expansion phase, stagflation, crisis and depression.

Secular cycles of Turchin and Nefedov

It appears natural to relate economic cycles to cycles of dissipative structures.The Danish physicist Per Bak has shown that they oscillate around a critical point. The different parts of a same structure oscillate at different frequencies. We can therefore see a full spectrum of oscillations whose magnitudes are ever greater as they are spread over a longer period of time.

In my presentation at the Shift Project (2), I identified economic cycles to Carnot cycles described by the traditional variables P, V, T, but for which P represents the Gibbs-potential I called economic potential, measuring what economists usually call « demand ». The variable V represents the « volume » of production (quantity of manufactured goods). Lastly, the T variable, which I called the « temperature » of the economy (see article # 49), can be identified with what economists call « supply ».

At any given time, the state of an economic system may be represented by a point in space (P, V, T). In my previous post, I showed that all the points lie on a surface described by an equation of the state of an economy. I showed the analogy between this equation of a state and that of condensable fluids. I deduced that, as a fluid, an economy can be condensed into two distinct phases that I have identified as an economy for rich people, and an economy for poor people. I have shown that, within a certain area shown in dark in the figure, the two economies are dissociated from one another.

The figure below is the same as the one in the previous post, but rotated 90 ° clockwise. The three coordinate axes are still P, T, V now referred to by their economic appellations of demand, supply and production. Economic production is an extensive quantity, it is now reported on a vertical axis as a function of the two intensive variables that are the supply (toward the back) and the demand (toward the left). The curves usually called « isothermals » are the lines along which the supply remains constant.

Economic output (production), as a function of supply (offre) and demand (Falaise de Sénèque = Seneca Cliff)

The circuit is an arbitrary economic cycle around the critical point C. Projected onto the output (production)/demand plane, its area represents the energy dissipated during a cycle. Being a positive value, the rotation is necessarily clockwise. By analogy with a fluid, the part of the cycle which is in the dark area has been represented by a « condensation isotherm », here a vertical line segment.

The dark area is in a vertical plane. It seems natural to identify it to a zone of collapsing economy, a zone called « Seneca Cliff » by Ugo Bardi (3). In this zone of instability, production collapses vertically, whatever the supply (temperature) or the related demand (pressure) is. We have seen (previous post) that, within this area, the economy separates into two phases, one for poor people and one for rich people, with no interactions between them. The collapse of output is accounted by the fact that supply can no longer meet demand because poor people cannot afford to buy what rich people produce. Gradually the whole population gets impoverished.

The economic cycle of the figure can be described and understood as follows: at the foot of the cliff, the economic output first goes to a minimum. This part of the cycle is characterized by a shortage of material goods and a growing demand. It is clearly identifiable as the depression phase of Turchin and Nefedov.

On the left-hand side of the cycle, the economic output begins to rise. This part is characterized by low wealth inequalities and an almost total absence of unemployment. The supply aims to meet the demand and the production increases. Peace and well-being increase, so populations tend to grow. This is the so-called expansion phase of Turchin and Nefedov.

Once satisfied, the demand tends to decline but, due to investments, supply continues. We arrive in the hot zone of the luxury economy. It follows laws that are similar to those of perfect gases. The supply maintains the demand in the same way that high temperatures maintain pressure in a boiler. Rich people are becoming more numerous, but gradually production stagnates and unemployment rises. This is Turchin and Nefedov’s stagflation phase.

Then we arrive at the top edge of the Seneca cliff where the economic output collapses. Companies go bankrupt, populations uprise and governments are overthrown. This is Turchin and Nefedov’s crisis phase.

Similar to Sisyphus, civilizations bear the burden of production along their economic ascension up to the top of the cliff, from where they see the fruits of their labor crumble. At the foot of the cliff, new civilizations take over.

(1) P. Turchin, S. Nefedov, Secular cycles, Princeton (2009). 
(2) See the video of the article # 75 and the text published in Res-Systemica, vol. 14, Article 01 (September 2015). 
See: http://www.theoildrum.com/node/8317 (Bardi’s Seneca Cliff)
For information, here is the list of the cycles described in the book of Turchin and Nefedov with the related period:
The Plantagenet cycle (1150-1485) 
The Tudor-Stuart cycle (1485-1730) 
The capétien cycle (1150-1450) 
The Valois cycle (1450-1660) 
Rome: The cycle of the republic (350-30 BC.) 
Rome: The cycle of the principate (30 av JC-285.) 
Russia: Moscow cycle (1460-1620) 
Russia: The Romanov cycle (1620-1922)