Inclusion of finite-temperature effects in a nonlinear description of strongly interacting many-body systems

We consider a class of quantum many-body systems which are coupled by one- and two-body interactions. Following our earlier work on deriving nonlinear field equations of motion for such systems, we incorporate the effects of finite temperature through a semiclassical free energy functional. We first obtain implicit analytical formulas for the entropy density which lend themselves to simple asymptotic expansions. We then study the effects of entropy in both homogeneous and inhomogeneous régimes. In the former case, critical amplitude rescaling, transition temperature shifts and crossover effects are found. In the latter case, saturation effects are shown to promote the emergence of spatial periodicities in 1D.