As far as I know, there is currently no semantic meaning assigned to the active span, other than that it will become the parent of any new span that does not have an explicit parent set.

I think it would be very interesting to assign the meaning of "this Span is currently actively being processed on this thread" to that. This would allow additional timings on the span to be collected, e.g. in addition to the current measure of "latency" that results from end - start, we would have a "processing duration" that indicates how long the span (or any child of it) has been active in total. E.g. currently the span with the longest latency could be due to some other operations unrelated to that Span being scheduled in between.

I could also imagine using an API like http://man7.org/linux/man-pages/man2/getrusage.2.html or https://docs.oracle.com/javase/8/docs/platform/jvmti/jvmti.html#GetCurrentThreadCpuTime to measure the CPU time (user/sys) that has been consumed by a Span's operation.