A simple model featuring a double well potential is used to represent a liquid that is quenched from an ergodic state into a history-dependent glassy state. Issues surrounding the application of the Jarzynski equality to glass formation are investigated. We demonstrate that the Jarzynski equality gives the free energy difference between the initial state and the state we would obtain if the glass relaxed to true thermodynamic equilibrium. We derive new variations of the Jarzynski equality which are relevant to the history-dependent glassy state rather than the underlying equilibrium state. It is shown how to compute the free energy differences for the nonequilibrium history-dependent glassy state such that it remains consistent with the standard expression for the entropy and with the second law inequality.