What operations does an SoC, for example, Snapdragon, perform when there are no tasks?

Question

Electronics

Maybe some internal operations or completely stopped?

Answer 1

The concept of the absence of tasks exists for the operating system (or other software with the beginnings of a supervisor). There is no concept of "no tasks" for the processor. Any processor always executes the next instruction it has in memory (in some cases, in a separate instruction memory).
It can execute an empty instruction (which does nothing) or change its mode of operation to some kind of Sleep or Low-Power. But he does it all on command!

Answer 2

how should SoC differ radically from a stand-alone processor in this regard?

Answer 3

If there is a power-down or something from this, then it goes into this mode. But as already said above - on command. Well, it depends on the architecture - whoever comes up with it, so it will work and will