To thermodynamically address quantum nanoscopic scenarios that involve very small heat sources and strong system-bath correlation, we suggest a new framework that is based on the principle of passivity. Passivity allows to get many thermodynamic inequalities that constrain observables that were so far outside the scope of thermodynamics. As an example we derive lower and upper bounds on the system-bath energy covariance in the Jaynes-Cummings model (spin-oscillator interaction). Using a stronger version of the passivity principle, we extend the second law to handle initial system-bath correlation (which is common in microscopic strong system-bath coupling scenarios). In addition, it is shown that passivity-based inequalities can detect "sub-Maxwellian” demons that apply a feedback that is too subtle to be detected using the standard second law. Finally an intrinsically quantum feature of strong passivity is exploited to assign a thermodynamic cost for quantum coherence generation.