  We investigate the fundamental limitations imposed by thermodynamics for
creating correlations. Considering a collection of initially uncorrelated
thermal quantum systems, we ask how much classical and quantum correlations can
be obtained via a cyclic Hamiltonian process. We derive bounds on both the
mutual information and entanglement of formation, as a function of the
temperature of the systems and the available energy. While for a finite number
of systems there is a maximal temperature allowing for the creation of
entanglement, we show that genuine multipartite entanglement---the strongest
form of entanglement in multipartite systems---can be created at any
temperature when sufficiently many systems are considered. This approach may
find applications, e.g. in quantum information processing, for physical
platforms in which thermodynamic considerations cannot be ignored.
