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The Jüttner distribution function for equilibrium relativistic fluids has two well-known limits, the non-relativistic limit at low temperatures and ultra-relativistic limit for high temperatures. Recently, the description of this transition in velocity space in the system, from a gaussian to a bimodal distribution was made by Mendoza et al. Physically, it is a transition between a regime where the relativistic energy is dominated by kinetic to another where the rest energy dominates. It has been found that the critical temperature at which the relativistic corrections becomes relevant, depends just on the dimension of the system, this allowed a description in terms of the theory of critical points (Montakhab et al.). In this contribution a review of the thermodynamic quantities that are only dependent on the ratio between temperature and critical temperature, and the dimension is made. We will also analyze the effects of critical temperature on dissipative processes in simple special relativistic fluids. Particularly, purely relativistic terms that are usually proportional to the number density gradient are studied. The transport coefficients can be written in terms of the transition temperature, this will allow us to identify the lower order relativistic effects just in terms of the dimension of the system. [ABSTRACT FROM AUTHOR]

We present the effective diffusion coefficient for the diffusion in a narrow generally asymmetric channel embedded on a curved surface, in the case of simple diffusion of pointlike particles without interaction and under no external forces. First, we define the diffusion equation for anisotropic diffusion involving a version of the Laplace-Beltrami operator. Then, we choose symmetric surfaces whose metric components only depend on one of the local coordinates and thus, apply the Kalinay- Percus' projection method. With this method one can project two-dimensional anisotropic diffusion into the corresponding effective one-dimensional generalized Fick-Jacobs equation to the lowest order. The perturbation series to all orders converges and as a general result the effective diffusion coefficient on a curved surface depending on the longitudinal local coordinate was obtained and is presented. It contains metric terms that can be related with the Gaussian curvature of the surface. We illustrate our results by studying asymmetric conical channel configurations on two surfaces, namely, the catenoid that is a minimal surface, and the pseudosphere that is a surface with negative constant curvature. [ABSTRACT FROM AUTHOR]

In this work we study a completely degenerated fermion gas at zero temperature employing a semi-classical approximation obtained from polymer quantum mechanics. Polymer quantum systems are quantum mechanical models quantized in a similar way as in loop quantum gravity. These models allow the study in a simplified way of the discreteness of space present in loop quantum gravity. We obtain the thermodynamic quantities modified by the polymer scale and we note that the corresponding Fermi energy is exactly the same as if one directly polymerizes the momentum pF. [ABSTRACT FROM AUTHOR]

Polymer quantum systems are quantum mechanical models quantized in a similar way as loop quantum gravity. These systems have allowed a more simple study of some characteristics of loop quantization including some thermal aspects. In this work we study the thermostatistics of an ensemble of one-dimensional hydrogen atoms in a Bohr-like polymer quantization. We obtain a modification of the heat capacity due to the polymer length scale. We also study the corresponding polymer modification of the ionization fraction of hydrogen in the recombination. [ABSTRACT FROM AUTHOR]

Polymer quantum systems are mechanical models quantized in a similar way as loop quantum gravity but in which loops/graphs resembling polymers are replaced by discrete sets of points. Such systems have allowed to study in a simpler context some novel aspects of loop quantum gravity. Although thermal aspects play a crucial role in cosmology and black hole physics little attention has been given to the thermostatistics of many body polymer quantum systems. In this work we explore how the features of a one-dimensional effective polymer gas, affect its microstate counting and hence the corresponding thermodynamical quantities. [ABSTRACT FROM AUTHOR]