question re: building muscles at a deficit

If I am on atkins, it doesn't have carbs to burn, and essentially forces my body to burn up its fat stores.

Aren't those sources of energy/calories?

Why wouldn't it be possible to grow muscles, if they are using the fat for fuel?

Technically you aren't putting more calories in, but isn't it burning the calories you've STORED FOR soooo long???

Isn't that the whole point of a deficit? Burn the calories stored?

I am finding it difficult to believe you'd have to actually eat more to make muscle.

PS I am not on atkins

Well, if you stretch the definition of bulk beyond all recognition, maybe.

  Also keep in mind the "newbie exception" - if you haven't trained with resistance before it's potentially possible to gain a pound or so of actual muscle protein in the first 6-12 weeks of working out since it's a unfamiliar stress on your body's systems and some of the feedback loops aren't yet fully established.

 But most of what people interpret as 'bulk' in the first few weeks will be things like increased muscle glycogen, intramuscular water retention, inflammation of the muscle fibre and other factors that don't involve the contractile protein in the muscle which will significantly outweigh the actual amount of muscle protein built.

 A male athlete age 19-23 with perfectly optimized training, nutrition and recovery can at most build about an ounce of muscle protein a day without chemical assistance. The female athlete maybe half that. (I've seen some papers attempting to calculate a theoretical max and they're mostly a mess since there's no way to account for all the variables that go into training. One paper claimed 28.03g as the max, but I think that's unwarranted precision - "about an ounce a day" seems a more practically useful guesstimate.) 

 Start changing those things - not being 19-23, not being male, not optimizing training, nutrition and recovery for the purpose of building muscle mass and you reduce the upper bounds of that drastically.