Perturbation and Variational Methods in Nonextensive Tsallis Statistics

A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very natural way following the Feynman proof for the usual statistical mechanics. The inequality turns out to be form-invariant with respect to the entropic index $q$. The method is illustrated with a simple example in classical mechanics. The formalisms developed here are expected to be useful in the discussion of nonextensive systems.Comment: revte

Gibbs' Paradox according to Gibbs and slightly beyond

The so-called Gibbs paradox is a paradigmatic narrative illustrating the necessity to account for the N! ways of permuting N identical particles when summing over microstates. Yet, there exist some mixing scenarios for which the expected thermodynamic outcome depends on the viewpoint one chooses to justify this combinatorial term. After a brief summary on Gibbs' paradox and what is the standard rationale used to justify its resolution, we will allow ourself to question from a historical standpoint whether the Gibbs paradox has actually anything to do with Gibbs' work. In so doing, we also aim at shedding a new light with regards to some of the theoretical claims surrounding its resolution. We will then turn to the statistical thermodynamics of discrete and continuous mixtures and introduce the notion of composition entropy to characterise these systems. This will enable us to address, in a certain sense, a "curiosity" pointed out by Gibbs in a paper published in 1876. Finally, we will �nish by proposing a connexion between the results we propose and a recent extension of the Landauer bound regarding the minimum amount of heat to be dissipated to reset one bit of memory

Is there a relationship between brain type, sex and motivation to learn science?

Whilst sex is considered to be one of the most significant factors influencing attitudes towards science, previous research seems to suggest that, at least in non-science classes, there is no correlation between sex and motivation to learn science. The present study investigates a mixed group of science and non-science students of upper secondary level. The data show that there is in fact no correlation between sex and motivation to learn science in this group, but that there is a highly significant positive correlation between the students' so-called brain type and their motivation to learn science. At the same time, male students show a more systemizing brain type whilst female students have a more empathizing one. Therefore, the brain type seems in fact to be a basic variable of motivation to learn science, as previous research suggests. Our intention was to explore if involving the science motivation questionnaire (SMQ) could be a strategy to confirm and extend this hypothesis, which seems to be the case. We consider this study as a pilot in preparation for a larger and more systematically sampled project