ROUGH DRAFT authorea.com/93924

# Tsallis Exercise

This whole week, I have been assisting to the “International Workshop on Nonlinearity, Nonequilibrium and Complexity: Questions and perspectives in Statistical Physics.” 1. Mainly, because Dr. Carlos Velarde insisted me to go. Nonetheless, I have to be really grateful because I got amused by the interesting ideas presented by all these remarkable scientists. In spite of, my lack of rigorous knowledge about arithmetics, linear algebra, thermodynamics, quantum physics, and other formalisms, I deeply enjoyed the discussed topics. In particular Dr. Tsallis’ speech. I was not able to understood the entire presentation, however, the particular point about how to characterize a complex behavior for a dynamical system, got my attention. Recently, I have been working with Dr. Carlos Gershenson in a method for wind speed forecasting in a wind farm located in Oaxaca, Mexico. Part of the analysis tried to prove that the behavior described by the wind speed data (hourly data, to be precise) is complex. I can’t give an exact description of complexity because I’m a noob in the area. However, I understand this concept as a system with a mixture of simple and non-simple behaviors. These, are triggered by normal or sporadic influences (self or external). Therefore, its behavior its said to be complex (niether simple nor too-erratic). Furthermore, they are predictable. This last statement is important, because we want to predict the wind speed! Another important thing for this anecdote is that, Dr. Tsallis said that positive Lyapunov exponents (an statistical measure about how a system diverge with two very close initial conditions), very small Lyapunov exponents, where an indicator of complex systems. So, the wind speed of this site at Oaxaca is complex, right? I already knew that, at least partially. With Dr. Gershenson we employed his entropic-measures, which are used to describe the complexity of discrete systems, to wind speed data. We concluded that the system is ’fairly complex’. However, during a presentation of the aforementioned work 2 some physicists doubted about the complexity of my system. So, motivated by all these, I approached Dr. Tsallis and talked him about this quandary. Before I describe you the exercise Tsallis proposed, first let me show you the data:

Now, the experiment consisted in 1. Obtain the logarithmic returns of wind speed, this is: $$\log(v_t/v_{t-1})$$