Resumo Este trabalho interdisciplinar propõe utilizar objetos astronômicos como ferramenta lúdica para despertar a curiosidade dos alunos, oportunizar e potencializar o processo de ensino-aprendizagem nas aulas de Física II e Mecânica Estatística. Seu objetivo consiste em discutir se a lei de distribuição de velocidades de Maxwell-Boltzmann para gases ideais também descreve o comportamento das velocidades das estrelas em aglomerados estelares. Para isso, os pensamentos investigativos dos alunos serão provocados com dados de velocidades de estrelas, obtidos através de observações do telescópio Blanco e KPNO (Observatório Nacional Kitt Peak), fornecidos na literatura para o aglomerado globular Ômega Centauri e para o aglomerado aberto Plêiades. Foi possível concluir que, em aglomerados globulares relaxados dinamicamente, embora possuam naturezas físicas muito diferentes da de gases ideais, as estrelas seguem a lei de distribuição de velocidades de Maxwell-Boltzmann. Isto ocorre porque, de fato, qualquer sistema clássico de muitos corpos que atenda as duas hipóteses usadas na dedução da distribuição de velocidades vai satisfazer a distribuição de Maxwell-Boltzmann, independente da interação entre os corpos serem de curto ou longo alcance e de serem objetos microscópios ou macroscópicos. Então, ao demonstrar que aglomerados de estrelas seguem leis semelhantes à dos gases ideais tornou-se possível utilizar o lúdico da Astronomia para incentivar os alunos no processo de aprendizagem do conteúdo de teoria cinética dos gases.

Abstract This interdisciplinary work proposes to use astronomical objects as a ludic tool to arouse student's curiosity, provide opportunities and enhance the teaching-learning process in Physics II and Statistical Mechanics classes. Its purpose is to discuss whether the Maxwell-Boltzmann velocity distribution law for ideal gases also describes the behavior of star velocities in star clusters. For this, the student's investigative thoughts it will be triggered by star velocity data, obtained through observations from the Blanco telescope and KPNO (Kitt Peak National Observatory), provided in the literature for the Omega Centauri globular cluster and the Pleiades open star cluster. It can be concluded that in dynamically relaxed globular clusters, although physically very different from ideal gases, stars follow Maxwell-Boltzmann's law of velocity distribution. This is because, in fact, any classical many-body system that satisfies the two assumptions used in the computations of velocity distribution will satisfy the Maxwell-Boltzmann distribution, regardless of whether the interaction between the bodies is of short or long-range and whether they are microscopic or macroscopic objects. Thus, by demonstrating that star clusters follow ideal gas-like laws, it became possible to use the ludic of astronomy to encourage students in the process of learning the content of the kinetic theory of gases.

The exact solution of the asymmetric exclusion problem and several of its generalizations is obtained by a matrix product ansatz. Due to the similarity of the master equation and the Schrodinger equation at imaginary times the solution of these problems reduces to the diagonalization of a one dimensional quantum Hamiltonian. Initially, we present the solution of the problem when an arbitrary mixture of molecules, each of then having an arbitrary size (s = 0; 1; 2; ...) in units of lattice spacing, diffuses asymmetrically on the lattice. The solution of the more general problem where we have the diffusion of particles belonging to N distinct classes of particles (c = 1; ... ; N), with hierarchical order and arbitrary sizes, is also presented. Our matrix product ansatz asserts that the amplitudes of an arbitrary eigenfunction of the associated quantum Hamiltonian can be expressed by a product of matrices. The algebraic properties of the matrices defining the ansatz depend on the particular associated Hamiltonian. The absence of contradictions in the algebraic relations defining the algebra ensures the exact integrability of the model. In the case of particles distributed in N > 2 classes, the associativity of this algebra implies the Yang-Baxter relations of the exact integrable model.