Authoritative Physics in Multiplayer

I want to make a simple multiplayer 2D platformer/shooter game, and run a dedicated server for it on my VPS. The VPS is very cheap (1 core CPU, 375mb RAM) so I’m not sure how to make the server for it. I thought about making an independent server program for it but then I’d have to write my own physics simulation and sync that with every player.

Is there a way to load a ‘Unity-lite’ library on a server program that’ll do all the physics work for me, but without rendering the entire game or using too much memory, so I can just do eg. “player1.position” and send that to every client?

Also relevant is I’d like to use Lidgren for the networking, will there be any conflicts with that?

TNet. Super simple. Server files are provided.