Nonlinear shear viscosity in two dimensions

In this paper we apply the transient-time-correlation function (TTCF) method to the calculation of the nonlinear shear viscosity of the two-dimensional soft-disk fluid. At low reduced strain rates ${(10\mathrm{}}^{\mathrm{-}8}$${<10\mathrm{}}^{\mathrm{-}2}$), the results are bounded by ‖$P_{\mathrm{xy}}$+η(0)γ‖∼${\eta }_2$ ${\gamma }^2$ and ‖p‖∼$p_2$ ${\gamma }^2$. For measurements of the shear stress at low strain rates, the TTCF method is clearly superior to the widely used subtraction technique. The differential TTCF method for calculating the intrinsically nonlinear response suffers, like the subtraction technique, from an exponential growth of noise.