Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, universal density-functional description, and nature of forces

Details Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, universal density-functional description, and nature of forces Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, universal density-functional description, and nature of forces

2011-08-23

arxiv.org/abs/1108.4536v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Resubmitted to Physical Review B. Extended with single-particle formulation based on universal density functionals and with a

Scientific paper

The standard formulation of tunneling transport rests on open-boundary modeling. Most theoretical studies of current-induced structural relaxations build from open-boundary calculations of electrostatic forces, omitting effects in the Gibbs free energy variation. A meaningful implementation of the Born-Oppenheimer approximation for tunneling systems requires, however, a consistent formulation of forces within a grand-canonical nonequilibrium (NEQ) thermodynamic theory, because the Friedel sum rule stipulates changes in total charge and because adiabatic transformations must be so slow that they also avoid an under-relaxed electron entropy content. In this paper I recast a formal NEQ thermodynamic theory for fully interacting tunneling systems, starting from the exact electron quantum kinetics account. I identify the operator for the Gibbs free energy and I define a variational NEQ thermodynamic grand potential functional which uniquely identifies the solution NEQ density matrix. I show that the uniqueness-of-density proof from a closely related Lippmann-Schwinger collision density functional theory [Phys. Rev. B 78, 165109 (2008)] makes it possible to express the variational NEQ thermodynamic description as a single-particle formulation based on universal electron-density functionals. The widely used atomistic ballistic-transport calculations [Phys. Rev. B 52, 5335 (1995)] of the electron density are found to represent a lowest-order approximation to the here-presented theory of interacting tunneling. From the variational theory, I furthermore define thermodynamic forces which are explicitly conservative, adiabatic, express an entropy maximization restricted by adherence to exact boundary conditions. I suggest that the here-described thermodynamic approach provides a more consistent implementation of forces in interacting tunneling.

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