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The standard formulation of tunneling transport rests on an open-boundarymodeling. There, conserving approximations to nonequilibrium Green function orquantum-statistical mechanics provide consistent but computational costlyapproaches; alternatively, use of density-dependent ballistic-transportcalculations [e.g., Phys. Rev. B 52, 5335 (1995)], here denoted `DBT', providecomputationally efficient (approximate) atomistic characterizations of theelectron behavior but has until now lacked a formal justification. This paperpresents an exact, variational nonequilibrium thermodynamic theory for fullyinteracting tunneling and provides a rigorous foundation for frozen-nuclei DBTcalculations as a lowest order approximation to an exact nonequilibriumthermodynamics density functional evaluation. The theory starts from thecomplete electron nonequilibrium quantum statistical mechanics and I identifythe operator for the nonequilibrium Gibbs free energy. I demonstrate a minimalproperty of a functional for the nonequilibrium thermodynamic grand potentialwhich thus uniquely identifies the solution as the exact nonequilibrium densitymatrix. I also show that a uniqueness-of-density proof from a closely relatedstudy [Phys. Rev. B 78, 165109 (2008)] makes it possible to provide asingle-particle formulation based on universal electron-density functionals. Iillustrate a formal evaluation of the thermodynamics grand potential valuewhich is closely related to the variation in scattering phase shifts and henceto Friedel density oscillations. This paper also discusses the differencebetween the here-presented exact thermodynamics forces and the often-usedelectrostatic forces. Finally the paper documents an inherent adiabatic natureof the thermodynamics forces and observes that these are suited for anonequilibrium implementation of the Born-Oppenheimer approximation.

journal of physics. condensed matter

Nonequilibrium thermodynamics of interacting tunneling transport:  variational grand potential, density-functional formulation, and nature of  steady-state forces