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The relativistic Poincaré model. (English. Russian original) Zbl 1186.83023
Dokl. Math. 80, No. 2, 769-774 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 428, No. 2, 171-176 (2009).
The paper considers the Poincaré model with relativistic corrections taken into account, i.e. a classical ideal gas consisting of relativistic particles. It is shown that the density of such a gas tends to a uniform density both as time unboundedly increases and decreases. Approximate equations describing the density evolution are obtained.
MSC:
83C10 Equations of motion in general relativity and gravitational theory
82D05 Statistical mechanics of gases
83A05 Special relativity
82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics
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References:
[1] H. Poincaré, in Selected Works (Nauka, Moscow, 1974) [in Russian].
[2] V. V. Kozlov, Thermal Equilibrium According to Gibbs and Poincaré (Izhevsk, 2002) [in Russian].
[3] V. V. Kozlov, Reg. Chaotic Dyn., No. 1, 23–34 (2004).
[4] V. V. Kozlov and O. G. Smolyanov, Teor. Veroyatn. Ee Primen. 51(2), 1–18 (2006).
[5] I. P. Pavlotskii, Foundations of Weakly Relativistic Statistical Mechanics (Vysshaya Shkola, Moscow, 1982) [in Russian].
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