  Recent studies have developed fundamental limitations on nanoscale
thermodynamics, in terms of a set of independent free energy relations. Here we
show that free energy relations cannot properly describe quantum coherence in
thermodynamic processes. By casting time-asymmetry as a quantifiable,
fundamental resource of a quantum state we arrive at an additional, independent
set of thermodynamic constraints that naturally extend the existing ones. These
asymmetry relations reveal that the traditional Szilard engine argument does
not extend automatically to quantum coherences, but instead only relational
coherences in a multipartite scenario can contribute to thermodynamic work. We
find that coherence transformations are always irreversible. Our results also
reveal additional structural parallels between thermodynamics and the theory of
entanglement.
