A method and apparatus that reduces the dead volume in a heat engine or heat pump, such as a duplex Stirling or Vuilleumier cycle device, by nesting the components of the displacer and regenerator such that nearly all working fluid is purged from the interstices of the regenerator elements and all other working fluid spaces that are not involved in doing useful work at each portion of the cycle. Particularly, a more scalable and efficient method and apparatus for providing solar air conditioning or refrigeration by means of a heated cylinder that alternately pressurizes and depressurizes a separate cooling cylinder by directly transferring thermally induced pressure changes to that cooling cylinder at optimized times in the cycle, under the control of a numerically controlled actuation system that can cycle at a much lower rate than mechanically coupled or harmonically phased systems.