Is viscosity a consequence of entropy? I have read viscosity defined: a) as diffusion of momentum, b) as dissipation of kinetic energy into heat, something like internal friction.
Is viscosity a consequence of the tendency of energy to diffuse, in other words of entropy?
 A: If you view this as a statistical mechanics problem, shear viscosity arises from the translational non-equilibrium in the flow (bulk viscosity is another effect). In other words, it arises because two layers of flow moving past one another have different average velocities of the molecules within them. 
So, we have two layers of fluids each with their own average velocities. Because these molecules also have thermal energy, a random velocity is superimposed on this mean -- this is just due to these molecules bouncing around randomly as they like to do. A molecule from the high speed side will, at some point, move into the low speed side and collide with a molecule there. This will transfer some kinetic energy from the high speed molecule to the low speed molecule. Likewise, some molecule on the low speed side will eventually bounce into the high speed side and collide. This will transfer energy again. 
As more and more of these molecules "change sides" and bring their average momentum with them, the difference in velocities between the two streams will be reduced. Eventually, when all of the molecules are moving the same speed, there is no viscosity because a molecule moving to one side is no different than the molecule it displaced. Statistically, it's the same state. 
So, looking at it from that perspective -- viscosity is caused by gradients of kinetic energy. It is, therefore, arising from the "tendency of energy to diffuse," but that's because molecules are discrete things and carry discrete amounts of energy with them. And when these molecules collide, they redistribute their energy between them. When the energy we are talking about is translational energy, you get viscosity. Other types of energy can be transferred as well, and these show up in the continuum equations as other material properties (molecular diffusivity, thermal diffusivity, etc). 
A: Viscosity appears in two forms: dynamic viscosity, which is what we normally mean by viscosity and kinematic viscosity $\nu$, which is the ratio of the viscosity of a fluid to its density.
You don't say if you want to distinguish between liquid viscosity and viscosity  in gases, I presume the former.
This area of physics is new to me, but having looked at my books, and sources such as Factors Affecting Viscosity and of course :) Wikipedia Viscosity, entropy is not directly mentioned.
But viscosity is only useful as a physical measurement if the temperature at which it's value is given is also stated.
As temperature can be defined as $1/T = \left(\frac {\partial S}{\partial U}\right)$ with $N$ and $V $ held constant, then you have an association between the degree of viscosity and entropy $S $.
