Starting from the BBGKY hierarchy, describing the kinetics of nonlinear particle system, we obtain the relevant entropy and stationary distribution function. Subsequently, by employing the Lorentz transformations we propose the relativistic generalization of the exponential and logarithmic functions. The related particle distribution and entropy represents the relativistic extension of the classical Maxwell–Boltzmann distribution and of the Boltzmann entropy, respectively, and define the statistical mechanics presented in [Phys. Rev. E 66 (2002) 056125] and [Phys. Rev. E 72, (2005) 036108]. The achievements of the present effort, support the idea that the experimentally observed power-law tailed statistical distributions in plasma physics, are enforced by the relativistic microscopic particle dynamics

PHYSICAL ORIGIN OF THE POWER-LAW TAILED STATISTICAL DISTRIBUTIONS / Kaniadakis, Giorgio. - In: MODERN PHYSICS LETTERS B. - ISSN 0217-9849. - STAMPA. - 26:10(2012), pp. 1250061-1-1250061-11. [10.1142/S0217984912500613]

### PHYSICAL ORIGIN OF THE POWER-LAW TAILED STATISTICAL DISTRIBUTIONS

#### Abstract

Starting from the BBGKY hierarchy, describing the kinetics of nonlinear particle system, we obtain the relevant entropy and stationary distribution function. Subsequently, by employing the Lorentz transformations we propose the relativistic generalization of the exponential and logarithmic functions. The related particle distribution and entropy represents the relativistic extension of the classical Maxwell–Boltzmann distribution and of the Boltzmann entropy, respectively, and define the statistical mechanics presented in [Phys. Rev. E 66 (2002) 056125] and [Phys. Rev. E 72, (2005) 036108]. The achievements of the present effort, support the idea that the experimentally observed power-law tailed statistical distributions in plasma physics, are enforced by the relativistic microscopic particle dynamics
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2498298`
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