By Murilo Bomfim
The Tsallis Controversy
In the 16th century, Copernicus said that the earth revolved around the sun. In the following century, Galileo Galilei confirmed this and therefore ended his life under house arrest. Almost four centuries later, another physicist came up with ideas that weren’t digested well – this time by his colleagues, not by the Church.
Today Constantino Tsallis is professor emeritus at the Brazilian Center for Physical Research in Rio de Janeiro. He was born in Greece and immigrated to Argentina. He did his PhD and taught at the University of Paris, where he settled in Brazil in 1975. Perhaps the shifts already heralded the theme of his life, the entropy or the degree of disturbance in a system.
Tsallis proposed a generalization of entropy. It is important to return home to explain. In contemporary physics, a major hypothesis is presented first, which is later opposed to a second theory. So it was with Newton’s mechanical theory. Applicable in several situations, it does not work well when analyzing objects that are moving at a speed close to that of light. The solution in this case came with Einstein’s theory of relativity. This process is called generalization: if the theory had a limitation before, it becomes generalized and can be applied to multiple situations.
Entropy, one of the pillars of physics, took shape with the Boltzmann-Gibbs theory, which in practice is used to analyze systems, measure their disturbance and make predictions. For example, the molecules of an ice cube are better organized than the vapor molecules, which move more and occupy more space – therefore they have more entropy. An ice cube is a simple system that is only affected by the pressure and temperature of the environment. How can one measure the entropy of complex systems related to strongly related factors?
In 1998, Tsallis published an article in the Journal of Statistical Physics suggesting the generalization of entropy (known as “Tsallis entropy”), a theory that could analyze complex systems. The controversy wouldn’t last long. “I was accused of tearing up a formula in physics that was crucial,” he says. “It was like saying that E = mc2 didn’t work in some cases.”
A renowned publication even recommended that the theory not be called “generalized entropy”. “Entropy is to physicists like Jesus is to Christians. Jesus cannot be generalized, ”said the editor, who was Jewish. Like Galileo, Tsallis became a heretic.
The research was a milestone in the physicist’s career – almost ten thousand citations are added today, making him the most cited Brazilian scientist (even if he is naturalized) in the world, according to Stanford University. But if the first few years of theory aroused curiosity and the search for tests, some time later the scientific community was divided: there are those who pulpit the idea, but there is no shortage of critics. The Greeks may have liked Tsallis, but physics seems like a field with multiple Trojans.
Most staunch opponents recognize the importance of the researcher, especially in the training of scientists, but claim that his theory is a simple mathematical modification of the Boltzmann-Gibbs formula. Adding a parameter to the original expression would only have created one tool. Over time, other solutions used in statistical physics would prove just as useful.
The questioners point out that Tsallis would not have created a physical model to explain a phenomenon as Einstein did with gravity. It would be like the equation helped define Jupiter’s position in the solar system, but lack of a physical basis has failed to explain why the planet is here and not there.
On the other hand, there are researchers in several countries who are working with Tsallis’ entropy trying to understand its best application niche. An example celebrated by the physicist took place in India: the analysis of mammograms, which was anchored in his theory, practically suppressed the results of the false positive type in microcalcifications (which cause the tumor).
In the end, Tsallis brought physics into a controversy that gave Mango a shawl – something considered healthy and inherent in scientific research. His most loyal followers continue to use his theory while others prefer to ignore it. Only time will tell whether Greeks or Trojans will win this battle.
Murilo Bomfim is a journalist.
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