1) White spots appear on the leaves. The spots almost have a silky texture that reminds me of a fungus. It almost seems like I can rub off the whiteness.
2) After a few days, the spots turn yellow then brown, then the entire stem starts to yellow.
3) Stem totally withers and falls off, but the rest of the plant appears healthy. My first plant even produced some fruit after almost all the leaves were gone!

The tomatoes are under a tree which MAY be a walnut (I'm not positive). Is it Walnut disease?

If it it is walnut disease, I can't do anything about it if the pots stay in their current locations. However, in the case that it isn't walnut disease, what else could it be? Here is some more info:

The spots and other symptoms happes generally from bottom to top.
I am careful not to water the leaves, and the soil is quite moist - daily waterings in the morning usually. It has been a pretty hot summer here in San Diego.
Other plants have not been affected (pea, cucumber, chili pepper).
They don't get that much sun, given that they are on my balcony :)

Any thoughts?

Thanks,

Jeremy

The tomatoes appear to be struggling for survival.

Are they in pots?
Are you fertilizing?
How do you determine when and how much to water?

The white stuff could be powdery mildew. This late in the season, I suggest you dump these plants than make an improved plan for next year's tomatoes.