Nonequilibrium Steady States and MacLennan-Zubarev Ensembles in a Quantum Junction System

Abstract

Based on a recent progress in nonequilibrium statistical mechanics of infinitely extended quantum systems, a nonequlibrium steady state (NESS) is constructed for a single-level quantum dot interacting with two free reservoirs under less general but more practically useful conditions than the previous works. As an example, a model of an Ahoronov-Bohm ring with a quantum dot is studied in detail. Then, NESS is shown to be regarded as a MacLennan-Zubarev ensemble. A formal relation between response and correlation at NESS is derived as well.stands for non-systematic energy flow, or heat flow, to the jth subsystem. A convergence factor e ǫs (ǫ > 0) is introduced in the time integral, where the limit ǫ → 0 is taken after all the calculations. As discussed in Ref. 2), this ensemble well describes nonequilibrium phenomena, but it has a fundamental difficulty. Indeed, because J S (s) is the sum of heat flows divided by subsystem tempertures, it is the entropy production rate of the whole system. Hence, if the ensemble (1 . 1) would describe a state consistent with the second law of thermodynamics, the average of J S (s) over ρ + should be a positive constant and, as a cosequence, the integral in (1 .

Nonequilibrium density matrix in quantum open systems: Generalization for simultaneous heat and charge steady-state transport

“…In the asymptotic limit, the NE density matrix will have matrix elements spreading over all the three different subspaces. Since the NE density matrix is independent of the initial conditions in the steady state [8][9][10][11][12][13][14][15] , one can take a convenient choice for the initial conditions that makes the derivations more easily tractable 45 . Finally, the left and right electrodes are prepared in a Gibbs grand-canonical ensemble with density matrices ρ α (α = L, R)…”

“…In such approaches, the Gibbsian statistical mechanics method is extended to include steady-state NE conditions in the density matrix leading to the so-called NE statistical operator method (NESOM). More rigorous analysis of the existence and stability of the NE steady state have been performed using C * algebraic methods [8][9][10][11][12][13][14][15][16] . The existence of conducting steady states has also been critically discussed in Refs.…”

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

“…The questions related to the possibility of reaching an NE steady-state have been addressed in [23][24][25][26][27][28][29][30][31]. It has also been argued that a system will always reach a steady-state if it is a (or if it is connected to another) system in the thermodynamic limit, regardless of the presence (or absence) of adiabatic switching of the interactions [32,33].…”

“…The quantity J S (s) is called the non-systematic energy flows [26] and is related to the entropy production rate of the system [25,26,49]. It is given by…”

“…In the literature, it is also customary to call J S,α the heat current with results from the energy flux [50]. Because J S (u) is the sum of heat flows divided by the subsystem temperature, it is the entropy production rate of the whole system [25,26]. The time integration of J S (u) in Equation (11) provides the asymptotic steady state value of the energy and charge fluxes J E α and J Q α , respectively.…”