Nonequilibrium density matrix for quantum transport: Hershfield approach as a McLennan-Zubarev form of the statistical operator

Abstract

In this paper, we formally demonstrate that the non-equilibrium density matrix developed by Hershfield for the steady state has the form of a McLennan-Zubarev non-equilibrium ensemble. The correction term in this pseudo equilibrium Gibbs-like ensemble is directly related to the entropy production in the quantum open system. The fact the both methods state that a non-equilibrium steady state can be mapped onto a pseudo-equilibrium, permits us to develop non-equilibrium quantities from formal expressions equivalent to the equilibrium case. We provide an example: the derivation of a non-equilibrium distribution function for the electron population in a scattering region in the context of quantum transport.

revised version - accepted for publication in PRE (Aug 2013)

References in corpus (9)

• Modeling inelastic phonon scattering in atomic- and molecular-wire junctions
• Superoperator nonequilibrium Green's function theory of many-body systems; Applications to charge transfer and transport in open junctions
• Imaginary-time formulation of steady-state nonequilibrium: application to strongly correlated transport
• Maximum-entropy theory of steady-state quantum transport
• Imaginary-time quantum many-body theory out of equilibrium I: Formal equivalence to Keldysh real-time theory and calculation of static properties
• Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density-functional formulation, and nature of steady-state forces
• Current-constraining variational approaches to quantum transport
• Non-equilibrium charge susceptibility and dynamical conductance: Identification of scattering processes in quantum transport
• Non-equilibrium statistical mechanics of classical nuclei interacting with the quantum electron gas

Cited by in corpus (17)

• Conformal field theory out of equilibrium: a review
• Thermodynamics of precision in quantum non equilibrium steady states
• Green's function methods for single molecule junctions
• Local Temperatures Out of Equilibrium
• Emergent second law for non-equilibrium steady states
• Quantum battery charging by non-equilibrium steady-state currents
• Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems
• Nonequilibrium density matrix for simultaneous heat and charge steady-state transport in quantum open systems
• Nonequilibrium distribution functions for quantum transport: universality and approximation for the steady state regime
• Linear response in large deviations theory: A method to compute non-equilibrium distributions
• Quantum thermodynamics of nanoscale steady states far from equilibrium
• Transport and thermodynamics in quantum junctions: A scattering approach
• Nonequilibrium fluctuation-dissipation relations for one- and two-particle correlation functions in steady-state quantum transport
• Contact geometry and quantum thermodynamics of nanoscale steady states
• Emergence of the Gibbs ensemble as a steady state in Lindbladian dynamics
• Nonequilibrium electron distribution function in a voltage-biased nanowire: A nonequilibrium Green's function approach
• Coherent transport through a resonant level coupled to random-matrix leads