-2 -1 0 0 2 4 (k ) $_{F}$a -2 dE/d(1/k ) GLYPH<c112> F a E -3 -2 -1 0 0.25 0.30 0.35 0.40 T+I V FIG. 3: Testing the adiabatic sweep theorem. (Inset) The measured potential energy, V , and release energy, T + I , per particle in units of E$_{F}$ is shown as a function of 1 /k$_{F}$ a . (Main) Taking a discrete derivative of the data shown in the inset, we find that 2 π dE d ( − 1 / ( k$_{F}$ a )) ( • ) agrees well with the contact C measured from the high- k tail momentum distribution ( ◦ ). interaction strength is changed adiabatically. To obtain the energy per particle, E , we sum the values for T + I and V shown in the inset of Fig. 3. To test the adiabatic sweep theorem, we find the derivative, dE d ( − 1 / ( k$_{F}$ a $_{))}$, simply by calculating the slope for pairs of neighboring points in the inset to Fig. 3. In the main part of Fig. 4, we compare this point-by-point derivative, multiplied by 2 π , to C obtained from the average values of the data shown in Fig. 2( ◦ ). Comparing these measurements of the left and right sides of Eqn. 2, we find good agreement and thus verify the adiabatic sweep theorem for our strongly interacting Fermi gas. A second universal relation that we can directly test is the generalized virial theorem [2], E − 2 V = T + I − V = − C 4 πk$_{F}$a , (3) which relates the difference between the release energy and the potential energy to the contact. Eqn. 3 is predicted to be valid for all values of the interaction strength ( k$_{F}$a ) − $^{1}$. This generalized virial theorem reduces to E − 2 V = 0 for the ideal gas, where I = 0, as well 8