More calories on workout days?

This is something I have been thinking about for a while now; when you are doing any kind of physical activity (lets say the Foundation courses) which way of the following two is ideal for the best strength gains:

Eating the same amount of calories each day or more calories on workout days and less on rest days?

Are there any studies on this? And what if the rest days include cardio?

Eating the same amount everyday is of course more simpler but I have been led to believe that eating more on workout days will help you gain more from the workout. Of course the weekly calories would be the same in both examples.

Thoughts on this?

I eat more on training days.

I don't conciously eat more on training days. I eat as I am hungry. Unless you are huge (or bored), you likely shouldn't have to focus on that.

Thanks for your input guys 

Do you need more gas on days you drive more? (rhetorical question that hopefully serves to make the necessary point)