Non-extensive entropy of Vinen quantum turbulence

TL;DR

This paper proposes that the vortex line ensemble in Vinen quantum turbulence can be described using non-extensive Tsallis-Cirto statistics, linking thermodynamics to flow velocity in superfluids.

Contribution

It introduces a novel application of non-extensive entropy to model the statistical structure of quantum turbulence in superfluids.

Findings

Vortex line ensemble follows Tsallis-Cirto statistics with δ=3.

Temperature relates to flow velocity as T∼mv^2.

Provides a new thermodynamic perspective on quantum turbulence.

Abstract

In Ref. [1] the statistical structure of the turbulent cascade in the context of non-additive entropy was considered. Here we suggest that the vortex line ensemble in the Vinen quantum turbulence in superfluids is described by the non-extensive Tsallis-Cirto statistics with $\delta=3$. This in particular leads to the temperature, which describes the thermodynamics of the Vinen ensemble, $T\sim mv^2$, where $v$ is the velocity of the flow and $m$ is the mass of the atom of the superfluid liquid.