Entanglement entropy of proton and its relation to thermodynamics entropy

I discuss the thermodynamics-based derivation of the formula for the entanglement entropy of a system of gluons. The derivation is based on an approach where saturation and the Unruh effect were used to obtain and discuss the entropy of gluons. The formula agrees, in the high-energy limit, up to a numerical factor, with more recent results, where arguments based on the density matrix and bipartition of the proton were used to obtain the formula. I also discuss the relation of entropy as obtained in BFKL in DLL approximation and with the application of the BK equation.