  Building on parallels between geometric quantum mechanics and classical
mechanics, we explore an alternative basis for quantum thermodynamics that
exploits the differential geometry of the underlying state space. We develop
both microcanonical and canonical ensembles, introducing continuous mixed
states as distributions on the manifold of quantum states. We call out the
experimental consequences for a gas of qudits. We define quantum heat and work
in an intrinsic way, including single-trajectory work, and reformulate
thermodynamic entropy in a way that accords with classical, quantum, and
information-theoretic entropies. We give both the First and Second Laws of
Thermodynamics and Jarzynki's Fluctuation Theorem. The result is a more
transparent physics, than conventionally available, in which the mathematical
structure and physical intuitions underlying classical and quantum dynamics are
seen to be closely aligned.
