  Quantum thermodynamics aims at investigating both the emergence and the
limits of the laws of thermodynamics from a quantum mechanical microscopic
approach. In this scenario, thermodynamic processes with no heat exchange,
namely, adiabatic transformations, can be implemented through quantum
evolutions in closed systems, even though the notion of a closed system is
always an idealization and approximation. Here, we begin by theoretically
discussing thermodynamic adiabatic processes in open quantum systems, which
evolve non-unitarily under decoherence due to its interaction with its
surrounding environment. From a general approach for adiabatic non-unitary
evolution, we establish heat and work in terms of the underlying Liouville
superoperator governing the quantum dynamics. As a consequence, we derive the
conditions that an adiabatic open-system quantum dynamics implies in the
absence of heat exchange, providing a connection between quantum and thermal
adiabaticity. Moreover, we determine families of decohering systems exhibiting
the same maximal heat exchange, which imply in classes of thermodynamic
adiabaticity in open systems. We then approach the problem experimentally using
a hyperfine energy-level quantum bit of an Ytterbium $^{171}$Yb$^+$ trapped
ion, which provides a work substance for thermodynamic processes, allowing for
the analysis of heat and internal energy throughout a controllable engineered
dynamics.
