1. A method for controlling a graphics processing unit coupled to a self-refreshing display device, the method comprising: detecting a trigger event that indicates that the display device is set to enter a self-refresh mode; in response to detecting the trigger event, determining whether any mutual exclusion mechanism in a set of mutual exclusion mechanisms is bound to a data object stored in a memory associated with the graphics processing unit, wherein the mutual exclusion mechanism prevents the data object from being accessed by two or more processes simultaneously; and if at least one mutual exclusion mechanism is bound to a data object, for each mutual exclusion mechanism bound to a data object, copying the data object and entering a deep sleep state, or if no mutual exclusion mechanisms are bound to a data object, then entering the deep sleep state without copying the data object.