Entanglement Energetics in the Ground State

We show how many-body ground state entanglement information may be extracted from sub-system energy measurements at zero temperature. A precise relation between entanglement and energy fluctuations is demonstrated in the weak coupling limit. Examples are given with the two-state system and the harmonic oscillator, and energy probability distributions are calculated. Comparisons made with recent qubit experiments show this type of measurement provides another method to quantify entanglement with the environment.