Export a sketch and have a look at the .java files generated if you really want to see what happens.

I don't know the finer details, but basically everything you put in your sketch's .pde files gets wrapped in to a class.

Code:

public class sketchNameHere extends PApplet { ... } 

This makes all the classes you write inner classes within this class, and I'm not sure if that is the reason you can't have static variables.

You can also have .java files in your sketch to do whatever you like.

See Environment in the Processing Reference; especially notes under:

• Sketchbook,
• Tabs, Multiple Files, and Classes
• Programming Modes
• Application Export

You can also use the Processing libraries from Eclipse, for example.

Check out Proclipsing for making life in Eclipse a little easier.

-spxl