Entanglement and thermodynamical analogies

We provide some new properties of entanglement of formation. In particular, we obtain an additive lower bound for entanglement of formation. Subsequently we develop the concept of local orthogonality of ensembles which leads to the mixed states with distillable entanglement equal to entanglement of formation. Then we consider thermodynamical analogies within the entanglement processing domain. Especially, we exploit analogy entanglement -- energy. In this scheme the total entanglement i.e. the amount of singlet pairs needed for local preparation of a state corresponds to internal energy while the free entanglement defined as the number of pairs which can be recovered from the state (distillable entanglement) is the counterpart of free energy. In particular, it leads us to the question about ``temperature'' of entanglement. We also propose a scheme of the search of representative state for given entanglement which can be viewed as an analogue of the Jaynes maximum entropy principle.