Ensino de Entropia: um enfoque histórico e epistemológico.

The rational construction necessary to systematize scientific knowledge in physics, introduces difficulties of understanding in some of its concepts. One of these concepts which exemplify properly this difficulty in learning or teaching is entropy. This thesis propose the construction of a didactic route which constitute itself a historical and epistemological course to entropy, intending to contribute for teaching this concept as well as other physics concepts. The basic assumption to build this route is that through the historical review of the development of this concept in the way suggested by Bachelard s (1884-1962) epistemology it is possible to make subjects, to be taught and learned, more meaningful. Initially I composed a brief biographical note to give the reader an idea about the issues, interests and reflections, related to science, and how I dealt with them in my private and professional life, as well as the role they played to lead me to write this thesis. The strategy to construct the route to entropy was to split the usual contents of basic thermodynamics in three moments in a way they can constitute epistemological units , which can be identified by the way of thinking in the corresponding moments of scientific knowledge production: a technical and empiricist moment, a rationalist and positivist moment and a post-positivist rationalist one. The transition between each moment is characterized by a rupture with the former way of thinking; however the progress in the construction of knowledge in the area is evident. As the final part of this work I present an analysis based on elements of Bachelard s epistemology that are present in each moment. This analysis is the basic component of the didactic route that I propose myself to build. The way I made this route guide to entropy could contribute to the construction of other didactic routes in physics and other sciences, in a way to unveil hidden meanings and as a tool to humanize scientific knowledge.

Análise em conjunta de testes cosmológicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Entropia de bloco no formalismo estatístico generalizado de Kaniadakis

A posição que a renomada estatí stica de Boltzmann-Gibbs (BG) ocupa no cenário cientifíco e incontestável, tendo um âmbito de aplicabilidade muito abrangente. Por em, muitos fenômenos físicos não podem ser descritos por esse formalismo. Isso se deve, em parte, ao fato de que a estatística de BG trata de fenômenos que se encontram no equilíbrio termodinâmico. Em regiões onde o equilíbrio térmico não prevalece, outros formalismos estatísticos devem ser utilizados. Dois desses formalismos emergiram nas duas ultimas décadas e são comumente denominados de q-estatística e k-estatística; o primeiro deles foi concebido por Constantino Tsallis no final da década de 80 e o ultimo por Giorgio Kaniadakis em 2001. Esses formalismos possuem caráter generalizador e, por isso, contem a estatística de BG como caso particular para uma escolha adequada de certos parâmetros. Esses dois formalismos, em particular o de Tsallis, nos conduzem também a refletir criticamente sobre conceitos tão fortemente enraizados na estat ística de BG como a aditividade e a extensividade de certas grandezas físicas. O escopo deste trabalho esta centrado no segundo desses formalismos. A k -estatstica constitui não só uma generalização da estatística de BG, mas, atraves da fundamentação do Princípio de Interação Cinético (KIP), engloba em seu âmago as celebradas estatísticas quânticas de Fermi- Dirac e Bose-Einstein; além da própria q-estatística. Neste trabalho, apresentamos alguns aspectos conceituais da q-estatística e, principalmente, da k-estatística. Utilizaremos esses conceitos junto com o conceito de informação de bloco para apresentar um funcional entrópico espelhado no formalismo de Kaniadakis que será utilizado posteriormente para descrever aspectos informacionais contidos em fractais tipo Cantor. Em particular, estamos interessados em conhecer as relações entre parâmetros fractais, como a dimensão fractal, e o parâmetro deformador. Apesar da simplicidade, isso nos proporcionará, em trabalho futuros, descrever estatisticamente estruturas mais complexas como o DNA, super-redes e sistema complexos

Iinterpretação conjunta de dados de GPR e medidas de permeabilidade sobre um análogo de reservatório siliciclástico falhado na bacia de Tucano, no NE do Brasil

It is presented an integrated geophysical investigation of the spatial distribution of faults and deformation bands (DB´s) in a faulted siliciclastic reservoir analogue, located in Tucano Basin, Bahia State, northeastern Brazil. Ground Penetrating Radar (GPR) and permeability measurements allowed the analysis of the influence of DB´s in the rock permeability and porosity. GPR data were processed using a suitable flow parametrization in order to highlight discontinuities in sedimentary layers. The obtained images allowed the subsurface detection of DB´s presenting displacements greater that 10 cm. A good correlation was verified between DB´s detected by GPR and those observed in surface, the latter identified using conventional structural methods. After some adaptations in the minipermeameter in order to increase measurement precision, two approaches to measure permeabilities were tested: in situ and in collected cores. The former approach provided better results than the latter and consisted of scratching the outcrop surface, followed by direct measurements on outcrop rocks. The measured permeability profiles allowed to characterize the spatial transition from DB´s to undeformed rock; variation of up to three orders of magnitude were detected. The permeability profiles also presented quasi-periodic patterns, associated with textural and granulometric changes, possibly associated to depositional cycles. Integrated interpretation of the geological, geophysical and core data, provided the subsurface identification of an increase in the DB´s number associated with a sedimentary layer presenting granulometric decrease at depths greater than 8 m. An associated sharp decrease in permeability was also measured in cores from boreholes. The obtained results reveal that radagrams, besides providing high resolution images, allowing the detection of small structures (> 10 cm), also presented a correlation with the permeability data. In this way, GPR data may be used to build upscaling laws, bridging the gap between outcrop and seismic data sets, which may result in better models for faulted reservoirs

Estudo da transição de fase da percolação através da entropia da informação

Various physical systems have dynamics that can be modeled by percolation processes. Percolation is used to study issues ranging from fluid diffusion through disordered media to fragmentation of a computer network caused by hacker attacks. A common feature of all of these systems is the presence of two non-coexistent regimes associated to certain properties of the system. For example: the disordered media can allow or not allow the flow of the fluid depending on its porosity. The change from one regime to another characterizes the percolation phase transition. The standard way of analyzing this transition uses the order parameter, a variable related to some characteristic of the system that exhibits zero value in one of the regimes and a nonzero value in the other. The proposal introduced in this thesis is that this phase transition can be investigated without the explicit use of the order parameter, but rather through the Shannon entropy. This entropy is a measure of the uncertainty degree in the information content of a probability distribution. The proposal is evaluated in the context of cluster formation in random graphs, and we apply the method to both classical percolation (Erd¨os- R´enyi) and explosive percolation. It is based in the computation of the entropy contained in the cluster size probability distribution and the results show that the transition critical point relates to the derivatives of the entropy. Furthermore, the difference between the smooth and abrupt aspects of the classical and explosive percolation transitions, respectively, is reinforced by the observation that the entropy has a maximum value in the classical transition critical point, while that correspondence does not occurs during the explosive percolation.

Estudo da transição de fase da percolação através da entropia da informação

Various physical systems have dynamics that can be modeled by percolation processes. Percolation is used to study issues ranging from fluid diffusion through disordered media to fragmentation of a computer network caused by hacker attacks. A common feature of all of these systems is the presence of two non-coexistent regimes associated to certain properties of the system. For example: the disordered media can allow or not allow the flow of the fluid depending on its porosity. The change from one regime to another characterizes the percolation phase transition. The standard way of analyzing this transition uses the order parameter, a variable related to some characteristic of the system that exhibits zero value in one of the regimes and a nonzero value in the other. The proposal introduced in this thesis is that this phase transition can be investigated without the explicit use of the order parameter, but rather through the Shannon entropy. This entropy is a measure of the uncertainty degree in the information content of a probability distribution. The proposal is evaluated in the context of cluster formation in random graphs, and we apply the method to both classical percolation (Erd¨os- R´enyi) and explosive percolation. It is based in the computation of the entropy contained in the cluster size probability distribution and the results show that the transition critical point relates to the derivatives of the entropy. Furthermore, the difference between the smooth and abrupt aspects of the classical and explosive percolation transitions, respectively, is reinforced by the observation that the entropy has a maximum value in the classical transition critical point, while that correspondence does not occurs during the explosive percolation.