  Navier-Stokes equations are known as hydrodynamic equations which take
account of effects of dissipations. There are, however, problems in the
relativistic Navier-Stokes equations, i.e. the equations violate causality.
Israel-Stewart equations, which evade the problems of Navier-Stokes equations
by introducing new parameters, such as the relaxation times, have recently been
used in describing the space-time evolution of the quark-gluon plasma produced
in high energy heavy ion collisions. The viscosities and the relaxation times
are related to each other by imposing entropy constraints on the system.
According to Boltzmann-Einstein principle, the probability distribution of the
fluctuation in the energy-momentum tensor is related to the entropy of the
system. Applying this principle to the entropy in Israel-Stewart theory, one
can obtain the ratios of the viscosities to the relaxation times. We evaluate
the ratios of the viscosities to the relaxation times in SU(3) lattice gauge
theory.

High Energy Physics - Lattice