Thermodynamical risk analysis from the negative entropy

James Watt Engine
James Watt Engine

Erwin Schrödinger in his book “What is Life?” introduced the concept of negative entropy. Neguentropy is a magnitude that measures the distance to normality of a distribution of probability. Given a certain mean and variance, the Gaussian distribution has the highest entropy, and then, neguentropy is always nonnegative.

This magnitude can be linked to the Gibbs’s Free Energy that defines the spontaneous character of a certain change in the structure of a system without change the volume and it is representing the competing effects of the enthalpic and entropic forces. In the same way that there is an amount of internal energy that can change without increasing the entropy or the volume, there is an amount of entropy that can be increased without changing the energy of the system or the volume and this is the macroscopic meaning of neguentropy.

Imagine a system composed by two adiabatic recipients joined by a pipe with a closed valve with gas a different pressure and temperature. This system is structured and its state is defined by four variables: two pressures and two temperatures, however, pressures and temperatures are dependent at constant volume, then, the state can be defined only by one variable that depend on the percentage of the total mass of gas in every recipient.


If we open the valve the system spontaneously will evolve to the state of maximum entropy that will be got when pressures and temperatures are equal in both recipients. The system has lost his initial structure and there will be only one possible macrostate. Now, the evolution to the previous state cannot be produced spontaneously. As the recipients are adiabatic the internal energy of the full system has not been able to change, and the change is provided by turning the stored neguentropy (related to Gibbs’s energy) due to the valve into entropy.

Gibbs’s energy is providing us with a way to analyze systemic problems. The higher the Gibbs’s energy is, the faster the way where a system evolves to a different structure. If the increment of the Gibbs’s energy between the two states had the opposite sign, the system would have been preserved at the initial state after opening the valve.

This scheme of analysis can provide us with a way to analyze economy defining properly the concepts. A thermodynamical system is a system that follows the rules of thermodynamics. In engineering, the concepts of temperature, pressure, volume, work, heat and so on where developed previously to statistical physics. All the thermodynamical magnitudes can be got from a statistical viewpoint. This can provide us with a method to analyze economic systems. We only need to find the proper meaning of temperature, pressure, volume, work, and heat for an economic system.

Energy is the capability to provide work. In engineering, work follows the mechanical concept and it is provided by the expansion of the volume of a gas that can be moving the piston of an engine. However, in economy the concept of work should not be referred to this conversion of the internal energy into mechanical one but the conversion of some kind of internal energy into the physical production of goods and services.

In economy, money is a kind of energy. The internal energy of the system should be seen as the value of the total assets of an economy (included immaterial assets as internal knowledge out of the accountancy) and money is one of them. The problem here should be to define value as an absolute magnitude. Business activity implies the use of this energy to provide some work, and as in an engine, it should be necessary to replenish the expense of energy with additional incomes from the environment. Business activity searches for the extraction of energy from its environment to provide production. The most probable changes at the economic system are those ones that increase the internal energy of the businesses. These ones tend to be produced spontaneously. Changes that reduce the internal energy of the business are driven by their environments instead of the businesses (they are driven by changes of the conditions of pressure and temperature from outside). Concepts as tax burden and competition are related to the thermodynamical conditions of pressure and temperature that can produce undesired results on the business when they are far from the nominal ones.

The second principle of thermodynamics establishes that the entropy of the universe cannot decrease. This is implying that we can decrease the entropy of the system only increasing the entropy of the environment. Environment is all that is out of our economic system of study. If we are ruling a company, environment will be competition, markets, government and nature. If we are ruling a country, environment will be other countries, financial markets and nature. And if we are studying the global economic system, environment will be only nature. Global economic system can run due to the introduction of natural resources for production that implies an increase of the entropy of the natural environment.

Going back to the example of gas recipients, connecting two isolated economic systems would drive to get uniformity in order to reach the state of maximum entropy, however, there is in every system an opposite trend to preserve some kind of structure that can be measured through neguentropy that is the negative entropy presented by Schrödinger.

If we can determine the difference between the free energy of the two structures we could forecast if the final state of the system would be uniform or isolated. Thermodynamics can explain why although you link the economies of several countries with a common currency, you cannot reach the state of uniformity. Neguentropy is preserving the structure of the system. This is what economists usually know as barriers for the commerce. For instance, the spread or the risk bonus of the debt of different countries is a result of this neguentropy, and it reflexes different regulation, different politics, different language, different culture, different distance for the distribution of products and other barriers to commerce that makes possible an economic structuration of Europe far from uniformity and many times cannot change in a natural way.

Entropy is related to the total number of possible microstates, and structure is related to a number of identifiable states at macro level. When entropy is low and neguentropy is high, all possible states at the macro level are near a set of mean values that can be understood as the structure of the system. When entropy is very high and neguentropy is very low we cannot see structure at the system.

Complexity can be seen as a kind of free energy, namely, is a portion of the total internal energy of the system that can provide work but is subject to an irreversible loss. You can consider that it is related to the region defined by the states at macro level in a multidimensional space where the system can fall providing different functionalities. This magnitude does not depend only on structured relationships. It depends on uncertainty too. Uncertainty is not bad itself because it lets to reach certain states that would not be reached in a fully structured system, the difference is that we cannot assure when we can reach a certain state, only that it is a possible one. Gambling is not the safest way to become rich; however, it is possible to become rich through gambling. In other words, the system can evolve through better paths than expected ones due to uncertainty, although we cannot control it with precision.

The economic systems usually work with a certain amount of complexity, however, a change of complexity could provide additional production through the destruction of a part of the structured activity. For instance, in an economic crisis, the lack of credit for a multiproduct company can be faced though the sale of some non-liquid assets used for the manufacturing of a product to continue with another part of the activity (you have turned non-liquid assets into liquid ones in order to be incorporated in the production of another product, for instance, in order to purchase raw materials). Those assets will never be able to be used again and their activity will be abandoned. You have preserved the production and the system running but you are reducing the possible working options for the company; however, you have increased the entropy of the system because you have turned neguentropy into entropy: liquid assets can be used for many things, physical ones can be used for a few ones, however, the extra available money will not drive the future benefit of the company in the same way as the executed investments can do if you do not apply it for other new investments.

This is similar to how a chemical reaction releases additional energy through a change of the configuration of atoms into molecules. A system has that potential of energy due to the configuration of its components and, when the reaction is produced spontaneously, it is freed as heat. This heat can be used later to provide work through an engine or it can be lost towards the environment.


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