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.