Conservative Force Fields in Nonextensive Kinetic Theory

Abstract

We investigate the nonextensive $q$-distribution function for a gas in the presence of an external field of force possessing a potential $U(\mathbf{r})$. 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.

Accepted for publication in Physica A; 12 pages, 2 figures

References in corpus (5)

• Non Linear Kinetics underlying Generalized Statistics
• Non-Gaussian equilibrium in a long-range Hamiltonian system
• Nonextensive Thermostatistics and the H-Theorem
• Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system
• Mixing and equilibration: Protagonists in the scene of nonextensive statistical mechanics

Cited by in corpus (5)

• Nonextensivity in nonequilibrium plasma systems with Coulombian long-range interactions
• The nonextensive parameter and Tsallis distribution for self-gravitating systems
• Test of Nonextensive Statistical Mechanics by Solar Sound Speeds
• Power Law Stellar Distributions
• Conservative Force Fields in Non-Gaussian Statistics