Ground state cooling is not possible given initial system-thermal bath factorization

In this paper we prove that a fundamental constraint on the cooling dynamic implies that it is impossible to cool, via a unitary system-bath quantum evolution, a system that is embedded in a thermal environment down to its ground state, if the initial state is a factorized product of system and bath states. The latter is a crucial but artificial assumption often included in many descriptions of system-bath dynamics. The analogous conclusion holds for 'cooling' to any pure state of the system.