Gibbsian theory of power law distributions

TL;DR

This paper extends Gibbsian statistical mechanics to describe marginally stable, non-thermal equilibrium power law distributions in collisionless plasmas with turbulence, introducing an ordering parameter and non-extensive entropy.

Contribution

It develops a generalized Gibbsian framework with an ordering parameter and non-extensive entropy to explain power law distributions in turbulent collisionless plasmas.

Findings

Power law distributions are linked to marginally stable Gibbsian equilibria.

A new entropy and partition function form are derived for dependent subsystems.

Redefinition of temperature in non-extensive systems is proposed.

Abstract

It is shown that power law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium which are expected to occur in collisionless plasmas containing fully developed quasi-stationary turbulence. Gibbsian theory is extended on the fundamental level to statistically dependent subsystems introducing an `ordering parameter' $\kappa$. Particular forms for the entropy and partition functions are derived with super-additive (non-extensive) entropy, and a redefinition of temperature in such systems is given.