Effective temperatures of a driven, strongly anisotropic Brownian system

We use Brownian dynamics computer simulations of a moderately dense colloidal system undergoing steady shear flow to investigate the uniqueness of the so-called effective temperature. We compare effective temperatures calculated from the fluctuation-dissipation ratios and from the linear response to a static, long-wavelength, external perturbation along two directions: the shear gradient direction and the vorticity direction. At high shear rates, when the system is strongly anisotropic, the fluctuation-dissipation-ratio-derived effective temperatures are approximately wave-vector independent, but the temperatures along the gradient direction are somewhat higher than those along the vorticity direction. The temperatures derived from the static linear response show the same dependence on the direction as those derived from the fluctuation-dissipation ratio. However, the former and the latter temperatures are different. Our results suggest that the presently used formulas for effective temperatures may not be applicable for strongly anisotropic, driven systems.