Relativistic H-theorem and nonextensive kinetic theory

Details Relativistic H-theorem and nonextensive kinetic theory Relativistic H-theorem and nonextensive kinetic theory

Aug 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003basbr..23r..56s&link_type=abstract

Boletim da Sociedade Astronômica Brasileira (ISSN 0101-3440), vol.23, no.1, p.56-57

Mathematics

Probability

Scientific paper

In 1988 Tsallis proposed a striking generalization of the Boltzmann-Gibbs entropy functional form given by [1]
(1) where kB is Boltzmann's constant, pi is the probability of the i-th microstate, and the parameter q is any real number. Nowadays, the q-thermostatistics associated with Sq is being hailed as the possible basis of a theoretical framework appropriate to deal with nonextensive settings. There is a growing body of evidence suggesting that Sq provides a convenient frame for the thermostatistical analysis of many physical systems and processes ranging from the laboratory scale to the astrophysical domain [2]. However, all the basic results, including the proof of the H-theorem has been worked in the classical non-relativistic domain [3]. In this context we discuss the relativistic kinetic foundations of the Tsallis' nonextensive approach through the full Boltzmann's transport equation. Our analysis follows from a nonextensive generalization of the "molecular chaos hypothesis". For q > 0, the q-transport equation satisfies a relativistic H-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by the relativistic Tsallis' q-nonextensive velocity distribution. References [1] C. Tsallis, J. Stat. Phys. 52, 479 (1988). [2] J. A. S. Lima, R. Silva, and J. Santos, Astron. and Astrophys. 396, 309 (2002). [3] J. A. S. Lima, R. Silva, and A. R. Plastino, Phys. Rev. Lett. 86, 2938 (2001).

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