We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients \eta and \zeta of the membrane fluid .
We show that the membrane pressure is intimately connected with Noether charge entropy S _ { { } _ { \mathrm { Wald } } } of the horizon when we consider a specific m -th order Lanczos-Lovelock model , through the relation p ^ { ( m ) } A / T = \left [ ( D - 2 m ) / ( D - 2 ) \right ] S ^ { ( m ) } _ { { } _ { \mathrm { Wald } } } , where T is the temperature and A is the area of the horizon .
Similarly , the viscosity coefficients are expressible in terms of entropy and quasi-local energy associated with the horizons .
The bulk and shear viscosity coefficients are found to obey the relation \zeta = -2 ( D - 3 ) / ( D - 2 ) \eta .