Stratification of air in a closed system vs the stack effect

[Elquery]

TL;DR

Would air, given a truly closed system, stratify by temperature? Is the stack effect relevant to closed systems, or is it specific to outside reference?

In thinking about temperature stratification of air: I assume that in a truly closed system with no heat inputs, air would NOT stratify by temperature.

On the other hand, a heat source introduced in a closed container would generate stratification while it was generating heat (and following for a time). It would then trend towards equilibrium (diffusion, entropy, etc.)

So temperature stratification is dependent on a dynamic system, and the trend is towards equilibrium: remove the source of heat, and stratification will actually REDUCDE not increase.
Yes?

Therefore, the more isolated a system is, the less temperature stratification we will observe. Yes?
Therefore, the 'stack effect' is a term most relevant to open systems. Indeed it is sometimes referred to as chimney effect, which implies a communication between two... steady states?

 

[Lnewqban]

Stratification of air inside a closed place tends to be a more or less static phenomenum.
Stack effect is dynamic, as a vertical movement is stablished due to difference of densities between two spaces.

Please, see:
https://en.m.wikipedia.org/wiki/Thermal_destratification

https://en.m.wikipedia.org/wiki/Stack_effect

I believe that you are correct about absence of stratification in an ideal closed system after certain period of time for equlibrium of temperature within the mass of gas or air to be reached.