Independent electron model for open quantum systems: Landauer-Büttiker formula and strict positivity of the entropy production

Nenciu, G.

doi:10.1063/1.2712418

Cited by 49 publications

(69 citation statements)

References 23 publications

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“…The formula for heat current is the same as that for energy current, Eq. (75), but with (E − µ i ) in place of E. Hence the heat current into the scatterer from reservoir i [56,86,[130][131][132] is…”

Section: The Basics Of Scattering Theorymentioning

confidence: 99%

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

et al. 2017

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In recent years, the study of heat to work conversion has been re-invigorated by nanotechnology. Steady-state devices do this conversion without any macroscopic moving parts, through steady-state flows of microscopic particles such as electrons, photons, phonons, etc. This review aims to introduce some of the theories used to describe these steady-state flows in a variety of mesoscopic or nanoscale systems. These theories are introduced in the context of idealized machines which convert heat into electrical power (heat-engines) or convert electrical power into a heat flow (refrigerators). In this sense, the machines could be categorized as thermoelectrics, although this should be understood to include photovoltaics when the heat source is the sun. As quantum mechanics is important for most such machines, they fall into the field of quantum thermodynamics. In many cases, the machines we consider have few degrees of freedom, however the reservoirs of heat and work that they interact with are assumed to be macroscopic. This review discusses different theories which can take into account different aspects of mesoscopic and nanoscale physics, such as coherent quantum transport, magnetic-field induced effects (including topological ones such as the quantum Hall effect), and single electron charging effects. It discusses the efficiency of thermoelectric conversion, and the thermoelectric figure of merit. More specifically, the theories presented are (i) linear response theory with or without magnetic fields, (ii) Landauer scattering theory in the linear response regime and far from equilibrium, (iii) Green-Kubo formula for strongly interacting systems within the linear response regime, (iv) rate equation analysis for small quantum machines with or without interaction effects, (v) stochastic thermodynamic for fluctuating small systems. In all cases, we place particular emphasis on the fundamental questions about the bounds on ideal machines. Can magnetic-fields change the bounds on power or efficiency? What is the relationship between quantum theories of transport and the laws of thermodynamics? Does quantum mechanics place fundamental bounds on heat to work conversion which are absent in the thermodynamics of classical systems?

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Section: The Basics Of Scattering Theorymentioning

confidence: 99%

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

et al. 2017

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“…Then at t = 0 they are suddenly joined together with a sample, and the newly composed system is allowed to freely evolve until it reaches a steady state at t = ∞. From a mathematical point of view this approach is by now very well understood, see for example [1,19,33,28,5] and references therein. One can allow the carriers to interact in the sample [18], and the theory still works.…”

Section: Generalitiesmentioning

confidence: 99%

Adiabatic Non-Equilibrium Steady States in the Partition Free Approach

Cornean

Duclos

Purice

2011

Ann. Henri Poincaré

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Consider a small sample coupled to a finite number of leads, and assume that the total (continuous) system is at thermal equilibrium in the remote past. We construct a nonequilibrium steady state (NESS) by adiabatically turning on an electrical bias between the leads. The main mathematical challenge is to show that certain adiabatic wave operators exist, and to identify their strong limit when the adiabatic parameter tends to zero. Our NESS is different from, though closely related with the NESS provided by the Jakšić-PilletRuelle approach. Thus we partly settle a question asked by Caroli et al in 1971 regarding the (non)equivalence between the partitioned and partition-free approaches.

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“…Now, using that (4.37) is a strictly decreasing function of σ j , one can prove [24] that the integrand of (4.34) is nonnegative 2 , implying the second law of thermodynamicsṠ ≥ 0 in the LB state for all (β i , µ i ) and scattering matrices (3.14). As explained in section 5.2 below, this argument does not apply to the other states of the orbit O β,µ and the entropy production there behaves indeed differently.…”

Section: Currents and Efficiencymentioning

confidence: 99%

Energy transmutation in nonequilibrium quantum systems

Mintchev¹,

Santoni²,

Sorba³

2015

J. Phys. A: Math. Theor.

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We investigate the particle and heat transport in quantum junctions with the geometry of star graphs. The system is in a nonequilibrium steady state, characterized by the different temperatures and chemical potentials of the heat reservoirs connected to the edges of the graph. We explore the Landauer-Büttiker state and its orbit under parity and time reversal transformations. Both particle number and total energy are conserved in these states. However, the heat and chemical potential energy are in general not separately conserved, which gives origin to a basic process of energy transmutation among them. We study both directions of this process in detail, introducing appropriate efficiency coefficients. For scale invariant interactions in the junction our results are exact and explicit. They cover the whole parameter space and take into account all nonlinear effects. The energy transmutation depends on the particle statistics.

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Independent electron model for open quantum systems: Landauer-Büttiker formula and strict positivity of the entropy production

Cited by 49 publications

References 23 publications

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

Adiabatic Non-Equilibrium Steady States in the Partition Free Approach

Energy transmutation in nonequilibrium quantum systems

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