Adam Smith, the 18th century father of modern economics, said that there was an “invisible hand” that guided players in a market, always seeking their own gain, to act, nevertheless, in a way that led to a better distribution of goods and better prices for the consumer than any effort specifically in that direction could have.
The laws of physics have it that any particle, stationary or in motion, interacts with other particles so that the energy of motion that it brings stays constant — either retained or passed on to the other particle. The other particle also follows this principle and the first particle may end up with more energy than it started with, but thanks to something given up by another particle. The result is that the speeds of millions of particles in motion — for example, the molecules of a gas distribute themselves so that there are very few particles with high energy or with low energy, but with a great many at a point in between. And this point can be shown to be the one where there is the greatest number of different ways for the particles, 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, report in the journal Entropy, their finding that the way energy use and also CO2 emissions are distributed in the world is just like the way energy is distributed among the molecules of a gas. This said, there follows the observation that thwo-thirds of all the energy produced is consumed by just one-third of the world population, who also produce two-thirds of all the CO2 emissions, per capita.
The paper in Entropy is based on US Information Administration International Energy Statistics, which show the historical and projected data of energy use and emissions, as in Figure 1. It can be seen that although there is an improvement in the efficiency of power generation, in terms of lesser emission, both power consumption and emission have been increasing, with the rising population. The paper notes that the energy consumption and population of developed countries have largely 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, as is shown by Figure 2. While the total consumption by developing countries is still less than by other countries, the inequality becomes acute if population is taken into account and countries are characterised by consumption per  capita.
The comparison of economic activity with the properties of the molecules of a gas comes about by treating 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 an 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. The proposition then 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 have, hence, been made of the distribution of income in the USA, UK, Australia, European Union countries, Romania and others, and the results have been 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 in the case of a gas.
For making a comparison between countries, the differences in currency and purchasing power have been gotten over by using the energy consumption per capita as representing physical living standards. Studies were first made using data of the World Resources Institute, of 130 countries from 1990 to 2005 and now, in the present work, with wider data from the US Energy Information Administration, which covers 220 countries over 1980 to 2010. In using energy consumption as a measure, the worldwide energy resources are being considered, first as redistributable and, second, as constant, and so 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 considered 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 in the journal attribute to globalisation of the world economy.
The distribution in 2010 is shown in Figure 3, 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.
Another representation of the data is with the help of the so-called Lorenz curve, 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.
There is a measure of inequality called the Gini coefficient (G) of the Lorenz curve, which measures how far the curve deviates from the ideal, diagonal, straight line. We can see that G=0 is the diagonal itself, where everything is equal, and the opposite is G=1, where all except one, who receives everything, receive nothing. 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 is again attributed to the globalisation of the economy in recent decades.
The authors draw a parallel with temperature inequality and the tendency of nature to equalise temperature, which amounts to dismantling an element of order, being the driving force in physical systems. This is also 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, inclusive 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 in the media of an “economic ice age”, the paper notes. While different causes have been suggested, the authors propose that the slowdown can be explained in terms of thermodynamics, as arising from falling inequality and increasing entropy.
On a brighter note, they ask if economic slowdown may bring in reduced carbon emissions and slowing climate change. But the progression from 1980 to 2010 only shows changes in distribution, not control of total emissions. Given the serious inequality that persists, the international parleys on climate change have had no effect in the last 20 years, while developed countries maintain high consumption and developing countries strive to “catch up”. The study also shows that inequality appears to be “intrinsic”, just as there is inequality in the motion of molecules of a gas. While the parallel with thermodynamics helps with insight into mechanisms at work, the answer may lie only in a changeover to renewable energy sources, viz, wind or solar, which are both emission-free and also equally distributed around the world, the authors say.

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