Is It Illegal to Run from Security Guards

My question involves criminal law for the state of: Georgia/New York

I do not shoplift and would never consider it. In fact, I have never stolen anything. I don't condone shoplifting nor do I think that shoplifters should run from security guards if caught. In fact, I think that shoplifters deserve to get caught as it hopefully teaches them a lesson not to continue shoplifting. Even from a purely Machiavellian standpoint, the small items that shoplifters generally steal are never even worth the risk of getting caught anyways. So, it's also stupid.

That being said, security guards are private citizens making a citizen's arrest when they detain you, correct? I have not heard of their being a law against resisting/fleeing a citizen's arrest. I've only heard of those laws applying to arrest by a peace officer. So, I'm thinking that perhaps if one were to run from them, there would be no additional charges for fleeing if their attempt to flee was unsuccessful or they were arrested later on. I'm also guessing that they could not chase a person outside of the property, as their liability insurance would presumably only cover their actions while on the property. Given the fact that citizen's arrests can lead to lawsuits, they would presumably be trained not to pursue the shoplifter after they leave the store. Of course, the security footage would show their face. Therefore, the police may find the shoplifter later on of course

Is It Illegal to Run from Security Guards