I'd like to achieve the following setup:

Every time I connect my laptop to a local network, my partition gets automatically mirrored to a partition on my local server.

I only want to mirror what has changed from the last time. (I understand that it is not a proper backup solution since there is no history of the changes, it'd be more like a non-persistent network RAID.)

Is there a distributed file system that allows such a setup? I've done some searching and it seems to me that most distributed file-systems are focused on data availability and distribution, not duplicating them.

I'd be thankful for suggestions.

Edit: Sorry, I forgot to mention: I'm using Linux.