  We propose a route towards engineering non-thermal states of matter, which
show largely unexplored physics. The main idea relies on the adiabatic passage
of a thermal ensemble under slow variations of the system Hamiltonian. If the
temperature of the initial thermal ensemble is either zero or infinite the
ensemble after the passage is a simple thermal one with the same vanishing or
infinite temperature. However, for any finite non-zero temperature intriguing
non-thermal ensembles can be achieved. We exemplify this in: (a) a single
oscillator (b) a dimerized interacting one dimensional chain of spinless
fermions, (c) a BCS-type superconductor and (d) the topological Kitaev chain.
We solve these models with a combination of methods; either exactly,
numerically using the density matrix renormalization group (DMRG) or within an
approximate functional renormalization group (FRG) scheme. The designed states
show strongly non-thermal behavior in each of the considered models. For
example, for the chain of spinless fermions we exemplify how long ranged
non-thermal power-law correlations can be stabilized and for the Kitaev chain
we elucidate how the non-thermal ensemble can largely alter the transition
temperature separating topological and trivial phases.
