The Minkowski vacuum perceived by an accelerated observer behaves like a fluid that has not only a finite temperature due to the Unruh effect, but also a finite shear viscosity. This viscosity is purely kinematical and is believed to be related to entanglement. We directly calculate shear viscosity using linear responce theory, find entropy density and viscosity/entropy ratio for massless Dirac and electromagnetic fields. Although viscosity and entropy separately are different for different types of fields, their ratio is the same for spins 0, 1/2 and 1 and is found to be 1/4*Pi in all considered cases, in accordance with the famous Kovtun-Son-Starinets (KSS) bound, inspired by string theory. This universality is of interest in the context of the problem of the correspondence between entanglement and Bekenstein-Hawking entropies. However, in contrast to string theory, where the saturation of the KSS-bound corresponds to strong interaction (large ’t Hooft coupling), in the case under consideration the fields are free. It is also shown that locally on the membrane surface corresponding to a stretched Rindler horizon, the viscosity/entropy ratio is half the KSS-bound and equals 1/8*Pi.