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We study heat transfers in a single level quantum dot strongly coupled tofermionic reservoirs and subjected to a time-dependent protocol modulating thedot energy as well as the dot-reservoir coupling strength. The dynamics isdescribed using nonequilibrium Greens functions (NEGFs) evaluated to firstorder beyond quasi-static driving. We show that any heat definition expressedas an energy change in the reservoir energy plus any fraction of thesystem-reservoir interaction is not an exact differential when evaluated alongreversible isothermal transformations, except when that fraction is zero.However, even in that latter case the reversible heat divided by temperature,namely the entropy, does not satisfy the third law of thermodynamics anddiverges in the low temperature limit. Our results cast doubts on thepossibility to define a thermodynamically consistent notion of heat expressedas the expectation value of some Hamiltonian terms.

On the nature of heat in strongly coupled open quantum systems