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We take the perspective of open quantum systems and examine from theirnonequilibrium dynamics the conditions when the physical quantities, theirrelations and the laws of thermodynamics become well defined and viable forquantum many body systems. We first describe how an open system nonequilibriumdynamics (ONEq) approach is different from the closed combined system +environment in a global thermal state (CGTs) setup. Only after the open systemequilibrates will it be amenable to conventional thermodynamics descriptions,thus quantum thermodynamics (QTD) comes at the end rather than assumed in thebeginning. We see the open system approach having the advantage of dealing withnonequilibrium processes as many experiments in the near future will call for.Because it spells out the conditions of QTD's existence it can also aid us inaddressing the basic issues in quantum thermodynamics from first principles ina systematic way. We then study one broad class of open quantum systems wherethe full nonequilibrium dynamics can be solved exactly, that of the quantumBrownian motion of $N$ strongly coupled harmonic oscillators, interactingstrongly with a scalar field environment. Here we focus on the internal energy,heat capacity and the Third Law. We show for this class of physical models,amongst other findings, the extensive property of the internal energy, thepositivity of the heat capacity and the validity of the Third Law from theperspective of the behavior of the heat capacity toward zero temperature. Theseconclusions obtained from exact solutions and quantitative analysis clearlydisprove claims of negative specific heat in such systems and dispelallegations that in such systems the validity of the Third Law ofthermodynamics relies on quantum entanglement.

Quantum thermodynamics from the nonequilibrium dynamics of open systems: energy, heat capacity and the third law