A novel thermodynamic cycle for adsorption heat pumps and chillers is presented. It shows a significant improvement of the internal heat recovery between the adsorption and the desorption half cycle. A stratified thermal storage, which allows for a temperature-based extraction and insertion of storage fluid, is hydraulically coupled with a single adsorber. The benefit is an increased efficiency by reusing the released heat of adsorption for regeneration of the adsorber and by rendering possible low driving temperature differences. For investigating the second law of this cycle, a dynamic model is employed. The transient behavior of the system and the respective losses because of driving temperature differences at the heat exchangers and losses due to mixing within the storage and to the surroundings are depicted in this one-dimensional model. The model is suitable both for analyzing this advanced cycle as well as for comparisons with other cycles.