We compute the shear viscosity(η) and entropy density(S) for two system:(1)the pion-nucleon gas with finite chemical potential in low temperature region of the hadronic phase;(2)the weak coupling real scalar field theories with O(1) symmetry, from these two case, we use the linearized Boltzmann equation to calculate shear viscosity and find that the behaviors ofη/s can describe the phase transitions, we speculate these η/s behaviors are general properties of fluid, QCD and cold atoms.
