Life cycle of a gas planet? I am interested in learning more about the (simplified) life cycle of gas planets which are not brown dwarfs (meaning less than 13 Jupiter masses). It obviously starts off with their creation within a protoplanetary disk. For Jupiter, things then happened quickly:

Jupiter formed in a geologic blink. Its rocky core coalesced less than a million years after the beginning of our solar system, scientists reported Monday in the Proceedings of the National Academy of Sciences. Within another 2 million or 3 million years, that core grew to 50 times the mass of Earth.

Source: Washington Post: Jupiter is oldest planet in solar system
But what happens afterwards? How long would a gas planet like Jupiter live (assuming that the central star of the system would not consume it)? What will happen to the radual density distribution over time? On which parameters (mass, radius, initial density, ...) does the evolution depend?
Related

Terminology question: gas giant vs gas planet
Will Jupiter eventually stop shrinking?
The life cycle is just one of gradual cooling and settling. The heavier elements will sink towards the centre; the planet will get slightly more dense - probably reaching about 90% of its current radius. It will essentially become a cold mini-white dwarf made mostly of hydrogen and helium and supported by cold electron degeneracy pressure. The density is probably not high enough for it to crystallise before differentiation of the chemical elements has completed.
The density profile will not change very much from what it is now. If anything the desnsity gradient will become slightly shallower become because a degenerate gas of heavier elements has more electrons per unit mass and so exerts a higher pressure for the same density. Since the thermal conductivity is extremely high then a temperature gradient will gradually be eliminated in the inner regions.
These processes take place on tens of billions of year timescales. Jupiter will be quite similar to the way it is now by the time the Sun becomes a white dwarf.