# On the Probable Interpretation of Anticorrelation between the Proton Temperature and Density in the Solar Wind

## TL;DR

This paper proposes that the anticorrelation between proton temperature and density in the solar wind arises from universal properties of strongly-nonequilibrium plasmas described by spin-type Hamiltonians, offering an alternative to hydrodynamical explanations.

## Contribution

It introduces an electrostatic turbulence model based on spin-type Hamiltonians to explain the universal anticorrelation in solar wind protons, contrasting with traditional hydrodynamical approaches.

## Key findings

- Anticorrelation is a universal property of strongly-nonequilibrium plasmas.
- Spin-type Hamiltonian models can explain the formation of anticorrelated distributions.
- The phenomenon may be responsible for observed solar wind properties.

## Abstract

The anticorrelated distributions of temperature and density of protons are a well-known property of the solar wind. Nevertheless, it is unclear till now if they are formed by some kind of the universal physical mechanism? Unfortunately, a straightforward comparison of the characteristic relaxation times for the temperature and density, on the one hand, and pressure, on the other hand, encounters the problem of inapplicability of the hydrodynamical approach in the situation when the free-path length of the protons is considerably greater than the spatial scale of the structures under consideration. To resolve this problem, some kinds of the MHD turbulence - reducing the effective free paths - are usually assumed. In the present paper, we use an alternative approach based on the electrostatic (Langmuir) turbulence, described by the mathematical formalism of the spin-type Hamiltonians, which was actively discussed in the recent time in the literature on statistical physics. As follows from the corresponding calculations, formation of the anticorrelated distributions of temperature and density is a universal property of the strongly-nonequilibrium plasmas governed by the spin-type Hamiltonians when they gradually approach the thermodynamic equilibrium. So, just this phenomenon could be responsible for the anticorrelations observed in the solar wind.