Hi.
Not sure what you mean by "automatic cleanup". Activities are active jobs, usually with a purpose: They are running, or waiting to run.
If there are active jobs without a legitimate purpose (usually the ENDED_OK or ENDED_EMPTY stuff) , you may want to change the settings of those jobs. Jobs can be set to deactivate themselves upon ending with no errors, or even on ending without any such condition.
Apart from that, you can bulk-select multiple jobs and disable them (you'll probably be best off sorting the activity window by the status column to do this, since marking a block of jobs in differing states may inhibit the showing of the context menu option). You may also want to bulk-disable in smaller chunks of hundreds of jobs, and not thousands of jobs at one time, since I've seen the later overwhelm the engine.
Last but not least, a cold start of the engine will probably disable all (really, all) active objects.
Hth,
Carsten