Adam Smith, the 18th century father of modern economics, said that the very motivation of the participants in a market — to seek their own gain — itself impels them to action that leads to better distribution of goods and prices for the consumer.

At a more mechanical level, the molecules of a gas, which are in constant and rapid motion, interact with other molecules when placed in a container.

These interactions are known to follow well-documented rules, particularly that the total energy of motion when one molecule bounces off another, remains constant.

One particle may hence end up with more energy than it started with, but only thanks to something given up by another particle.

The second particle is then likely, in the next encounter, to regain the energy lost.

The way the speeds of the molecules distribute themselves, finally, is that very few particles have high or low energy but a great many have a level of energy that falls in between.

This level of most common particle energy can be shown to be the one where there is the greatest number of different ways for the molecules, with various speeds of motion, to have the same total energy.

It could also be called the point of most equitable distribution of energy, given the dynamics of collisions and the conservation of total energy.

Victor M Yakovenko, Qin Liu and Scott Lawrence, of the Joint Quantum Institute, department of physics, at the University of Maryland, have drawn a parallel between the way molecules of a gas tend to share energy and the way incomes, energy use and CO2 emissions tend to be distributed among the populations of the world.

They reported their findings, some months ago, in the journal, Entropy.

The paper in is based on the US Information Administration International Energy Statistics, which show the historical and projected data, of energy use and emissions.

Although there is improvement in the efficiency of power generation, in terms of lesser emission, both power consumption and emission have been increasing, with rising population.

The paper notes that the energy consumption and population of developed countries have stabilised and it is the developing world, like China for energy, and India and others for population, which account for the global increase.

This trend, however, is the result of great energy inequality among countries. While the total consumption by developing countries is still less than other countries, the inequality becomes acute if population is taken into account and countries are characterised by consumption per capita.

To see if the gas laws could help in understanding economic activity, the researchers treated the money with an individual as equivalent to the speed of a molecule.

In transactions between individuals, like in collisions of molecules, there would be exchange and redistribution of money. The comparison is valid because the total money in a system, like the total energy in a gas, is conserved, or stays constant, for some time.

The proposition was that after allowing for the possibility of debt, which does not exist in molecules of a gas, money also distributes itself, with mathematical precision, in the same way as the speed of molecules.

In studies of actual distribution of money, to verify the notion, there is a difficulty of different currencies and purchasing power, in cross border comparison.

Studies were therefore made of the distribution of income in the US, UK, Australia, EU countries, Romania and others — the results are that the distribution of the number of persons in increasing income ranges, in most cases, over a group of 97 per cent of the population, is exactly like energy in the case of a gas.

For the comparison between countries, the differences in currency and purchasing power were not accounted for by taking the energy consumption per capita to represent physical living standards.

The studies used data of the World Resources Institute, of 130 countries from 1990 to 2005 and from the US Energy Information Administration, which covers 220 countries over 1980 to 2010.

In using energy consumption as a measure, the world-wide energy resources were considered as redistributable and as constant, as also the population of countries, at least for a time.

The proposition again, is that the proportion of persons with higher energy consumption should fall, as the level of energy consumed is raised, in the same way as the distribution of the molecules of a gas.

The data is found to strongly support the proposition and the current data shows a progression from highly unequal distribution in 1980 to more uniform, and closer to theory, distribution in 2010 — a feature which the authors of the paper attribute to globalisation of the world economy. The distribution in 2010 is shown in figure 1, which plots the falling numbers of people who consume increasing levels of energy in the 220 countries studied.

The average energy consumption in the main countries of the world is also indicated. A revealing representation of the data is with the help of the so-called Lorenz curve (figure 2), which plots the fraction of energy consumption against fraction of the population at that level of consumption.

The curves for different years, 1980, 1990, 2000 and 2010 have been shown. A case where the numbers of consumers increase uniformly as we consider larger fractions of energy would be complete equality and this is the straight, diagonal line in the graph.

The other lines — the curves — indicate actual conditions, from 1990 to 2010, with the deviation from the ideal reducing every decade.

How far the Lorenz curve deviates from the ideal, diagonal, straight line indicates the level of inequity and is measured by a metric called the Gini coefficient — abbreviated as G — of the Lorenz curve.

One can see that G=0 is the diagonal itself, where everything is equal, and the opposite is G=1. The figure shows that the G value has been falling from 0.66 to 0.55, approaching the value of G=0.5, which is the equilibrium state of natural distribution, with large numbers of interactions and transactions, as in a volume of gas.

The fall from 0.66 to 0.55 indicates reducing inequality and is attributed to the globalisation of the economy in recent decades. The authors drew a parallel with temperature inequality and the tendency of nature to equalise temperature, which amounts to the dismantling of an element of “order” being the driving force in physical systems.

This can also be stated as the tendency to maximise disorder, and another word for the level of disorder is entropy.

The authors note that developed countries now have ageing populations and reducing consumption, including of energy, and stagnating growth.

But developing countries, China particularly, have become rising consumers of energy, per capita. And even this growth is slowing down and there is talk of an “economic ice age”, the paper noted.

While different causes have been suggested, the authors propose that the slowdown appears to be intrinsic and, in terms of thermodynamics, arises from falling inequality and increasing entropy.

On a brighter note, they ask if economic slowdown may bring in reduced carbon emissions and slow down climate change.

The progression from 1980 to 2010, however, only shows changes in distribution, not control of emissions.

While the parallel with thermodynamics helps with insight into the mechanisms at work, population control and using renewable energy sources may allow growth and economic activity without affecting the environment.

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