A compressor and heat pump combination has an active chamber and a passive chamber, each with its own hot plate and cold plate. The two chambers are joined along an edge by a membrane that largely transmits pressure, largely insulates against temperature transfer, and prevents passage of gases from one chamber to the other. The gas in the active chamber is alternately cooled and heated by exposure to the active cold and active hot plates, causing pressure changes in the active chamber that are transmitted to the passive chamber by the membrane. The pressure changes alternately cool the gas in the passive chamber below the temperature of the passive cold plate, and heat the gas in the passive chamber above the temperature of the passive hot plate. In alternately exposing the cooled gas in the passive chamber to the passive cold plate, and the heated gas in the passive chamber to the passive hot plate, heat is forced to flow from the passive cold plate to the passive hot plate. Other thermodynamic apparatus including stand alone compressors and heat pumps are described.