Conservative Force Fields in Nonextensive Kinetic Theory

TL;DR

This paper derives a nonextensive $q$-distribution function for gases under external forces, revealing how potential energy influences the distribution and applying it to planetary atmospheres, highlighting differences from classical thermodynamics.

Contribution

It introduces a rigorous derivation of the power law distribution with potential energy in nonextensive kinetic theory, extending the understanding of long-range interactions.

Findings

Maximum atmospheric height depends on the nonextensive parameter q.

In the extensive limit, the classical exponential Boltzmann distribution is recovered.

The model provides insights into the structure of planetary atmospheres under nonextensive conditions.

Abstract

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