Cooling and heating in the Bose-Hubbard model by parameter tuning

We investigate short-range interacting Bosons in an optical lattice at finite temperature. It is well known that the system shows a Mott-Superfluid transition when changing the repulsion U, the hopping t and/or the filling. However, it is much less clear how the temperature is affected by those changes, assuming the parameters U and/or t are tuned adiabatically. We now present higher order calculations for the full Free energy and derive the temperature and entropy in a large parameter space. We discuss where significant heating or cooling effects can be expected in the superfluid phase, in the Mott region and near the phase transition lines.