Phase transitions and perfectness of fluids in weakly coupled real scalar field theories

We calculate the ratio η/s$\eta /s$, the shear viscosity (η) to entropy density (s  ), which characterizes how perfect a fluid is, in weakly coupled real scalar field theories with different types of phase transitions. The mean-field results of the η/s$\eta /s$ behaviors agree with the empirical observations in atomic and molecular systems such as H₂O, He, N, and all the matters with data available in the NIST database. These behaviors are expected to be the same in N   component scalar theories with an O(N)$O(N)$ symmetry. We speculate these η/s$\eta /s$ behaviors are general properties of fluid shared by QCD and cold atoms. Finally, we clarify some issues regarding counterexamples of the conjectured universal bound η/s?1/4π$\eta /s?1/4\pi$ found in Refs. T.D. Cohen, Phys. Rev. Lett. 99 (2007) 021602, hep-th/0702136; A. Cherman, T.D. Cohen, P.M. Hohler, arXiv: 0708.4201 hep-th]; A. Dobado, F.J. Llanes-Estrada, Eur. Phys. J. C 51 (2007) 913, hep-th/0703132]