wait/arrive seems obvious to me. So I'll talk about that... As a synchronization primitive, its very useful for things like:

    parallel_memset(data, 0); // The 1024 threads go off and, in parallel + some efficient manner, initialize the datastructure
    barrier(); // wait for all 1024 threads to reach here before continuing.
    do_stuff(); // This probably relies on all default data being set before starting

I don't know what a "cluster" is, but its clearly some new subdivision of threads (aside from wavefront, group, block, grid, etc. etc.). Because locking is so inefficient on GPUs, you probably want to use barriers in the typical case.

Cluster arrive + Cluster wait allow for you to split the barrier into two units. Maybe the first half of a loop must be synchronized, but there's "spare extra work" you can do before calling wait(). This likely makes threading smoother.

    parallel_memset(data, 0); // The 1024 threads go off and, in parallel + some efficient manner, initialize the datastructure
    arrive();
    do_spare_work(); // some extra work before checking for a wait
    wait(); // We ran out of main work + spare work, so now we must fully stop and wait
    do_stuff(); // This probably relies on all default data being set before starting

This is likely more efficient for a number of algorithms than a singular barrier.

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As far as the L2 cache thing specifically: I don't know.