  In thermodynamics, quantum coherences - superpositions between energy
eigenstates - behave in distinctly nonclassical ways. Recently mathematical
frameworks have emerged to account for these features and have provided a range
of novel insights. Here we describe how thermodynamic coherence splits into two
kinds - "internal" coherence that admits an energetic value in terms of
thermodynamic work, and "external" coherence that does not have energetic
value, but instead corresponds to the functioning of the system as a quantum
clock. For the latter form of coherence we provide dynamical constraints that
relate to quantum metrology and macroscopicity, while for the former, we show
that quantum states exist that have finite internal coherence yet with zero
deterministic work value. Finally, under minimal thermodynamic assumptions, we
establish a clock/work tradeoff relation between these two types of coherences.
This can be viewed as a form of time-energy conjugate relation within quantum
thermodynamics that bounds the total maximum of clock and work resources for a
given system.
