If bacteria managed to arrive then thrive somehow (if not already) on a gas giant could it cause the atmosphere to expand or contract in volume?
Would living matter potentially induce energy into the planets system to heat it up?
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Yes, but probably not by a huge amount. There are two obvious ways this could happen:
Direct change in atmospheric composition. If our microbe does something like eat methane and excrete longer-chain hydrocarbons, that's going to eventually change the atmosphere enough to have some effect. (If the hydrocarbons weren't already forming, they probably aren't stable under local conditions, so there will be some equilibrium reached, the way the Earth's atmosphere isn't 100% oxygen despite hundreds of millions of years of photosynthesis.) Change in solar heat balance. The change in atmosphere will probably also change the amount of greenhouse effect (one way or the other), and second-order effects or even just enough microbial biomass can change the albedo (again, either way). On Earth, these effects can combine to change the temperature by tens of Kelvins, which would be a few percent different in atmospheric volume.
In neither case is the added life going to change the total mass of the atmosphere.