A simple thermodynamical witness showing universality of macroscopic entanglement

We show that if the ground state entanglement exceeds the total entropy of a given system, then this system is in an entangled state. This is a universal entanglement witness that applies to any physical system and yields a temperature below which we are certain to find some entanglement. Our witness is then applied to generic bosonic and fermionic many body systems to derive the corresponding "critical" temperatures that have a very broad validity.