Stability of families of probability distributions under reduction of the number of degrees of freedom

TL;DR

This paper investigates how certain probability distributions for ideal gas configurations maintain their form when degrees of freedom are reduced, exploring their connection to Tsallis' thermostatistics.

Contribution

It introduces classes of distributions that are stable under reduction of degrees of freedom and discusses their relation to Tsallis' thermostatistics.

Findings

Distributions depend only on kinetic energy.

Distributions remain form-invariant under degrees of freedom reduction.

Connection to Tsallis' thermostatistics is established.

Abstract

We consider two classes of probability distributions for configurations of the ideal gas. They depend only on kinetic energy and they remain of the same form when degrees of freedom are integrated out. The relation with equilibrium distributions of Tsallis' thermostatistics is discussed.