"degree of freedom" (singular)?

[Stephen Tashi]

Is it common terminology to refer to a state variable as a "degree of freedom"?

From the current Wikipedia article on degrees of freedom :

In physics, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all dimensions of a system is known as a phase space, and degrees of freedom are sometimes referred to as its dimensions.

https://en.wikipedia.org/wiki/Degrees_of_freedom_(physics_and_chemistry)

Edit: Another example of using "degrees of freedom" to mean a set of variables:

For a given system, the wave function is a complex-valued function of the systems degrees of freedom, continuous as well as discrete.

http://en.wikipedia.org/wiki/Wave_function

 

[Bystander]

state variable as a "degree of freedom"?

In thermodynamics, Gibbs' Phase Rule; describing states of other systems by specification of three coordinates and three momenta for every particle in the system, yes.

 

[Stephen Tashi]

It's interesting that "degrees of freedom" has two different definitions. In some contexts, it means the cardinality of the set of state variables. (e.g. http://en.wikipedia.org/wiki/Degrees_of_freedom_(mechanics) ) rather than the set of state variables itself.