  Current methods to describe the thermodynamic behavior of many-particle
systems are often based on perturbation theory with an unperturbed system
consisting of free particles. Therefore, only a few methods are able to
describe both strongly and weakly correlated systems along the same lines. In
this article we propose a cumulant approach which allows for the evaluation of
excitation energies and is especially appropriate to account for the
thermodynamics at low temperatures. The method is an extension of a cumulant
formalism which was recently proposed to study statical and dynamical
properties of many-body systems at zero temperature. The present approach
merges into the former one for vanishing temperature. As an application we
investigate the thermodynamics of the hole-doped antiferromagnetic phase in
high-temperature superconductors in the framework of the anisotropic t-J model.
