A relation between diffusion,temperature and the cosmological constant

TL;DR

This paper establishes a relationship between diffusion processes, temperature, and the cosmological constant in an expanding universe, showing that the fluid's temperature approaches a constant linked to the Hubble parameter and diffusion constant.

Contribution

It derives a novel connection between the fluid temperature in a diffusing universe and the cosmological constant, providing a new perspective on de Sitter thermodynamics.

Findings

Fluid temperature approaches T=κ²/H in de Sitter stage

Cosmological constant relates to diffusion constant as Λ=6πκ²

Final equilibrium temperature matches de Sitter horizon temperature

Abstract

We show that the temperature of a diffusing fluid with the diffusion constant \kappa^{2} in an expanding universe approaches a constant limit T=\kappa^{2}/H in its final de Sitter stage characterized by the horizon 1/H determined by the Hubble constant. If de Sitter surface temperature in the final equilibrium state coincides with the fluid temperature then the cosmological constant \Lambda=3H^{2}=6\pi\kappa^{2}.