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Quantum thermodynamics aims at investigating both the emergence and thelimits of the laws of thermodynamics from a quantum mechanical microscopicapproach. In this scenario, thermodynamic processes with no heat exchange,namely, adiabatic transformations, can be implemented through quantumevolutions in closed systems, even though the notion of a closed system isalways an idealization and approximation. Here, we begin by theoreticallydiscussing thermodynamic adiabatic processes in open quantum systems, whichevolve non-unitarily under decoherence due to its interaction with itssurrounding environment. From a general approach for adiabatic non-unitaryevolution, we establish heat and work in terms of the underlying Liouvillesuperoperator governing the quantum dynamics. As a consequence, we derive theconditions that an adiabatic open-system quantum dynamics implies in theabsence of heat exchange, providing a connection between quantum and thermaladiabaticity. Moreover, we determine families of decohering systems exhibitingthe same maximal heat exchange, which imply in classes of thermodynamicadiabaticity in open systems. We then approach the problem experimentally usinga hyperfine energy-level quantum bit of an Ytterbium $^{171}$Yb$^+$ trappedion, which provides a work substance for thermodynamic processes, allowing forthe analysis of heat and internal energy throughout a controllable engineereddynamics.

Quantum thermodynamics in adiabatic open systems and its trapped-ion experimental realization