着【zhe】

着 after a verb says a state is holding. The action already happened; what the sentence reports is the situation it left behind.

开着 is not the act of opening – it is the door standing open afterwards.

着 against 在

在 is an action under way; 着 is a state that persists. The pair is easiest to see on the same verb:

Verbs of posture, position and holding – 坐, 站, 拿, 带, 开, 关, 穿 – take 着 naturally. Verbs of motion mostly do not.

Two actions at once

V着 on the first verb makes it the manner of the second. The main verb comes last.

Reversing them changes which action is the main one.

Something present in a place

The place comes first, the thing last, the same order as 有.

Negation

没 plus the verb, with 着 kept.

For an instruction not to hold the state, 别 is used: 别站着，坐吧.