arXiv subjects
Publications and source records attributed to R. Silva.
The negative nature of the heat capacity $C_V$ of thermodynamically isolated self-gravitating systems is rediscussed in the framework of a non-extensive kinetic theory. It is found that the dependence of $C_V$ on the non-extensive parameter $q$ gives rise to a negative branch with the critical value corresponding to $q = 5/3$ ($C_V\to - \infty$).
The concept of Jeans gravitational instability is rediscussed in the framework of nonextensive statistics and its associated kinetic theory. A simple analytical formula generalizing the Jeans criterion is derived by assuming that the unperturbed self- gravitating collisionless gas is kinetically described by the $q$-parameterized class of power law velocity distributions. It is found that the critical values of wavelength and mass depend explicitly on the nonextensive $q$-parameter. The standard Jeans wavelength derived for a Maxwellian distribution is recovered in the limiting case $q$=1. For power-law distributions with cutoff, the instability condition is weakened with the system becoming unstable even for wavelengths of the disturbance smaller than the standard Jeans length $λ_J$.
The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the ``molecular chaos hypothesis". For $q>0$, the $q$-transport equation satisfies an $H$-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' $q$-nonextensive velocity distribution.
We investigate the nonextensive $q$-distribution function for a gas in the presence of an external field of force possessing a potential $U({\bf r})$. In the case of a dilute gas, we show that the power law distribution including the potential energy factor term can rigorously be deduced based on kinetic theoretical arguments. This result is significant as a preliminary to the discussion of long range interactions according to nonextensive thermostatistics and the underlying kinetic theory. As an application, the historical problem of the unbounded isothermal planetary atmospheres is rediscussed. It is found that the maximum height for the equilibrium atmosphere is $z_{max} = K_{B}T/mg(1-q)$. In the extensive limit, the exponential Boltzmann factor is recovered and the length of the atmosphere becomes infinite.
We discuss the basic transport phenomena in gases and plasmas obeying the $q$-nonextensive velocity distribution (power-law). Analytical expressions for the thermal conductivity ($K_q$) and viscosity ($η_q$) are derived by solving the Boltzmann equation in the relaxation-time approximation. The available experimental results to the ratio {$K_q$}/$η_q$ constrains the $q$-parameter on the interval $0.74 \leq q \leq 1$. In the extensive limiting case, the standard transport coefficients based on the local Gaussian distribution are recovered, and due to a surprising cancellation, the electric conductivity of a neutral plasma is not modified.
Maxwell's first derivation of the equilibrium distribution function for a dilute gas is generalized in the spirit of the nonextensive q-statistics proposed by Tsallis. As an application, the q-Doppler broadening of spectral lines due to the random thermal motion of the radiating atoms is derived.
The first-order general relativistic theory of a generic dissipative (heat-conducting, viscous, particle-creating) fluid is rediscussed from a unified covariant frame-independent point of view. By generalizing some previous works in the literature, we derive a formula for the temperature variation rate, which is valid both in Eckart's (particle) and in the Landau-Lifshitz (energy) frames. Particular attention is paid to the case of gravitational particle creation and its possible cross-effect with the bulk viscosity mechanism.