The debated rapport between thermodynamics and quantum mechanics will be  addressed in the framework of the theory of periodically driven/controlled quantum thermodynamic machines. The basic models studied by us are  a two-level system (TLS) or a harmonic oscillator, whose energy is periodically modulated while the system is coupled to two distinct thermal baths. When the modulation interval is short compared to the bath memory time, the system–bath correlations are affected, thereby causing cooling or heating of the TLS, depending on the interval [1,2]. This  setup constitutes the simplest (minimal)  quantum heat machine (QHM) that may operate as either an engine or a refrigerator, depending on the modulation/driving rate [3]. It is  used  by us to scrutinize basic thermodynamic principles in the quantum domain:

  (i) It is possible to  surpass the Carnot bound when the driving is done by a quantum device (piston) in an appropriate state [4-6]. However, such  enhanced efficiency does not mean that quantum effects invalidate the Carnot bound: their classical analog is a non-thermal bath whose temperature is controlled by its state. By contrast, engines powered by non-thermal (e.g. squeezed) baths may cease to be heat machines and act instead as devices exchanging work rather than heat with the baths, so that the Carnot bound is inapplicable to such devices [7].

(ii) An extension of the TLS model of quantum  heat machines  to multiple entangled TLS shows that the power output can be boosted by the  quantum cooperativity of these systems, but  the efficiency is still bounded by Carnot [6] .

(iii) The refrigeration effected by  such QHMs persists as the temperature approaches absolute zero for certain quantized baths, e.g., magnons, thus challenging  the Third Law(Nernst's unattainability principle) [2].

Thus, we may conclude that  quantum  machines powered by thermal and non-thermal baths  may benefit from hitherto unexploited quantum resources, but they still comply with traditional thermodynamic rules, possibly with the exception of  the Third Law.