Title: Magnetocaloric and electrocaloric properties of the Hubbard pair cluster

Abstract: The paper contains the discussion of the magnetocaloric and electrocaloric effect in a model dimer (pair cluster). The system of interest is modelled with a Hubbard Hamiltonian including the external electric and magnetic field. The thermodynamics of such pair is described exactly, on the grounds of the grand canonical ensemble, focusing on the half-filling of energy states. The quantities of interest, such as magnetic entropy, magnetic specific heat as well as isothermal entropy change resulting from the variation of either electric or magnetic field and appropriate Gr\"uneisen ratios are calculated and discussed in a wide range of external fields. The importance of singlet to triplet transition for the observed behaviour is emphasized. The ranges of direct and inverse caloric effects are found and the manifestations of the magnetoelectric phenomena are described. In particular, the tunability of the magnetocaloric effect with electric field as well as tunability of the electrocaloric effect with magnetic field are demonstrated.