A four-process cycle is disclosed for a Vuilleumier heat pump that has mechatronically-controlled displacers. Vuilleumier heat pumps that use a crank to drive the displacers have been previously developed. However, mechatronic controls provides a greater degree of freedom to control the displacers. The four-process cycle provides a higher coefficient of performance than prior cycles in the crank-driven Vuilleumier heat pump and those previously disclosed for a mechatronically-driven Vuilleumier heat pump. The four-process cycle can be drawn out to provide a low demand condition by causing both displacers to remain stationary for a period of time. The four processes in which one of the displacers is commanded to move are separated by periods of inactivity in which both displacers remain stationary.