Abstract
We show that the temperature of a diffusing fluid with the diffusion constant κ^{2} in an expanding universe approaches a constant limit T=κ^{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 Λ=3H^{2}=6πκ^{2}.
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