Abstract
The study of the fields particle number density, pressure and internal energy per particle - or simply energy per particle - in equilibrium gives precious preliminary information on the behavior of a gas described by an equilibrium distribution function. This information is useful not only when the gas actually is in a state of homogeneous equilibrium, but also when the main behavior is described in a sufficiently accurate way by an equilibrium distribution function; we shall see in the next few chapters several instances of this situation and the conditions under which it occurs. This topic is usually paid a lip-service in the non-relativistic case, because the fields to be studied are simply related; in the relativistic case rather complicated functions of at least one parameter occur (in the simplest case only modified Bessel functions show up).
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References
M. Abramowitz and I. A. Stegun, Handbook of mathematical functions (Dover, New York, 1968).
S. Chandrasekhar, An introduction to the study of stellar structure (Dover, New York, 1958).
J. P. Cox and R. T. Giuli, Principles of stellar structure, Vols. I and II, (Gordon and Breach, New York, 1968).
I. S. Gradshteyn and I. M. Ryzhik, Tables of integrals, series and products 5th ed. (Academic Press, San Diego, 1994).
S. R. de Groot, W. A. van Leeuwen and Ch. G. van Weert, Relativistic kinetic theory (North-Holland, Amsterdam, 1980).
D. C. Kelly, The kinetic theory of a relativistic gas, unpublished report (Miami University, Oxford, 1963).
G. M. Kremer, lima introdução à teoria cinética relativística (Editora da UFPR, Curitiba, 1998).
P. T. Landsberg and J. Dunning-Davis, Statistical thermodynamics of the ideal relativistic quantum gas, in Statistical mechanics of equilibrium and non-equilibrium pp. 36–51, ed. J. Meixner (North-Holland, Amsterdam, 1961).
P. T. Landsberg and J. Dunning-Davis, Ideal relativistic Bose condensation Phys. Rev. A 138, 1049–1052 (1965).
R. K. Pathria, Statistical mechanics 2nd. ed. (Butterworth-Heinemann, Oxford, 1996).
S. L. Shapiro and S. A. Teukolsky, Black holes, white dwarfs and neutron stars, (John Wiley and Sons, New York, 1983).
A. Sommerfeld, Zur Elektronentheorie, der Metalle auf Grund, der Fermischen Statistik, I. Teil: Allgemeines, Strömungs-und Austrittsvorgänge Z. Physik 47, 1–82 (1928).
J. M. Stewart, Non-equilibrium relativistic kinetic theory, Lecture Notes in Physics, vol. 10 (Springer, Heidelberg, 1971).
J. L. Synge, The relativistic gas (North-Holland, Amsterdam, 1957).
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© 2002 Birkhäuser Verlag
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Cercignani, C., Kremer, G.M. (2002). Fields in Equilibrium. In: The Relativistic Boltzmann Equation: Theory and Applications. Progress in Mathematical Physics, vol 22. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8165-4_3
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DOI: https://doi.org/10.1007/978-3-0348-8165-4_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9463-0
Online ISBN: 978-3-0348-8165-4
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