Entropy and economic inequality
In our imperfect society there is a lot of inequality. In recent years, economic inequality has been escalating at an alarming rate and the worldwide population is questioning the distribution of wealth. Recent economic crises, climate change, and the COVID-19 pandemic, are tearing down a pillar of modern society - the free market [1,2]. Unfortunately, winnowing economic inequality appears to be a difficult task.
The point at issue is whether increasing economic inequality is an inevitable outcome of civilization and technological progress, or if it’s possible to contain it by simmering down the economic growth without hindering technological development.
The predominant opinion is that in a free market, income inequality arises naturally due to the presence of driving forces, or what the British economist John Maynard Keynes called "animal spirits", such as ambition, fame, instincts, consumer spending, satisfaction, competition and making profit. After all, Artur Schopenhauer argued that the universe is the expression of a voracious irrational force, the will, that in living beings manifests itself as “Wille zum Leben”, the will to live.
These underlying forces constitute what Adam Smith, the father of modern economics, called "the invisible hand", that dovetails a modern society. Scrutinizing his contemporary society, Adam Smith conceived the idea that the pursuit of one's own selfish interest can promote the development of society. “It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own self-interest. We address ourselves not to their humanity but to their self-love, and never talk to them of our own necessities, but of their advantages.” [3] According to Adam Smith, an employer doesn’t hire personnel because of benevolence, but because he is seeking to make a profit using human labor. On the other hand, employees do not work to help out their boss, but because they need a salary.
We could be tempted to apply the laws of physics to the driving forces of the economy in order to construct models that can help us understand the complex contraption that is the economy. In fact, there is a connection between economy, energy transformation and entropy. This has transformed traditional economics. In recent years, a new interdisciplinary research field has emerged, the econophysics [4], which merges economics and physics. This new wrinkle stemmed from considering people as gas particles bouncing inside a box. Under this model, economic agents exchange money when they “collide”. What is meant here is that instead of applying mathematical models that take into account the rationality of an individual in order to elaborate strategies, we consider the entire society as a large thermodynamic system of economic agents bounded by constraints, e.g. money conservation, and apply the laws of thermodynamics and the tools of statistical mechanics. In such a system, the distribution of resources is subjected to the maximization of the entropy. In statistical mechanics, entropy is defined as a measure of the number of ways a system can be arranged. The more possible configurations are available to the system, the higher the entropy. A natural evolution of a system involves an increase in entropy, i.e. an increase in the number of the possible configurations.
According to the statistical definition of entropy, an evolution towards an equal distribution of resources would be very unlikely. In fact, in the case of equality, there is only one possible configuration in which individuals have the same amount of resources, while an unequal distribution of resources has many more configurations. Maximizing the entropy of the money distribution, using the Lagrange method and under the constraint of money conservation, Drăgulescu and Yakovenko find out that the equilibrium probability distribution of money (P(m)) is given by the Boltzmann-Gibbs distribution, P(m)=Ce^(-m/T) [5]. Here m is the money balance, T is the “money temperature”, defined as the average amount of money per economic agent and C is a normalizing constant.
Figure 1. Representation in arbitrary units of the equilibrium probability distribution of money, given by the Boltzmann-Gibbs distribution P (m) ∝e^(-m/T), at different money temperatures.
As we can see from the graph in Figure 1, the Boltzmann-Gibbs distribution describes an unfair world where the poor people are so far more than the rich ones. Economic inequality springs from entropic forces. Nedjeljka Pertic suggested that when thermodynamics is applied to society, entropy can be interpreted as freedom of individuals [6]. If there are no laws protecting the working class, a capitalist will exploit the labor force as much as possible in order to pursue profit maximization.
It’s a common thought that capitalism will always work because the only thing it requires from us is simply to listen to our egoistic interests, vices and worst instincts. As Luigi Pirandello wrote in the Pleasure of Honesty: “We ride through life on the beast within us. Beat the animal, but you can't make it think.” All the past communist regimes that have attempted to beat the animal have failed and it is believed communism will always fail.
However, even though Adam Smith argued that self-interest can be of benefit to the economy, in The Theory of Moral Sentiments, he extolled virtue, prudence, justice and beneficence. You are free to make as much profit as you want but your employees must not be forced to urinate in bottles [7].
References
1. https://time.com/5956255/free-market-is-dead/
2. https://www.theguardian.com/commentisfree/2019/apr/25/capitalism-economic-system-survival-earth
3. A. Smith, An Inquiry into the Nature & Causes of the Wealth of Nations, Vol 1.
4. V. M. Yakovenko, Econophysics, Statistical Mechanics Approach to, In: Meyers R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY (2009).
5. A. Drăgulescu and V.M. Yakovenko, Statistical mechanics of money, Eur. Phys. J. B 17, 723–729 (2000).
6. N. Pertic, Application of Thermodynamic theory to social events, Int. Rev. Mod. Sociol. Vol. 21 (1991, Spring).