Its a bit more complex than that. I can only speak for my aircraft (737NG) but its an electrically driven motorised door that opens outwards. Its got several motors and controlled by several controllers to prevent failure. The pressurisation system is a bit more sophisticated and picks a cabin altitude depending on your cruise level, field elevation etc. It then modulates the outflow to maintain whatever its looking for, beit steady or say 500fpm cilmb/descend etc.
Not sure what we're allowed to link to here, but there's some good descriptions and pictures here -
Pressurisation
There are also negative and positive pressure relief valves which are just mechanical devices.