TY - JOUR

T1 - Fundamental aspects of steady-state conversion of heat to work at the nanoscale

AU - Benenti, Giuliano

AU - Casati, Giulio

AU - Saito, Keiji

AU - Whitney, Robert S.

N1 - Funding Information:
We would like to express our gratitude to V. Balachandran, R. Bosisio, K. Brandner, M. Büttiker, S. Chen, R. Fazio, V. Giovannetti, C. Goupil, F. Haupt, M. Horvat, Ph. Jacquod, F. Mazza, C. Mejía-Monasterio, H. Ouerdane, T. Prosen, R. Sanchez, U. Seifert, J. Splettstoesser, G. Strini, F. Taddei, S. Valentini, and J. Wang, with whom we have had the pleasure of collaborating on the topics discussed in this review paper. We thank P. Hofer, B. Sothmann, R. Uzdin and an anonymous referee for comments that greatly improved this review. G.B. and G.C. acknowledge the support of the MIUR-PRIN. G.B. acknowledges the financial support of the INFN through the project “QUANTUM”. K.S was supported by JSPS KAKENHI ; grant numbers JP25103003 and JP26400404 . R.W. acknowledges the financial support of the COST Action MP1209 “Thermodynamics in the quantum regime” and the CNRS PEPS Energie grant “ICARE” . Appendix A
Publisher Copyright:
© 2017 Elsevier B.V.

PY - 2017/6/9

Y1 - 2017/6/9

N2 - 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.

AB - 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.

KW - Andreev reflection

KW - Dynamical quantum systems

KW - Entropy production

KW - Finite-time thermodynamics

KW - Linear response

KW - Master equations

KW - Non-equilibrium thermodynamics

KW - Onsager relations

KW - Peltier cooling

KW - Quantum Hall effect

KW - Quantum dots

KW - Quantum point contacts

KW - Quantum thermodynamics

KW - Quantum transport

KW - Scattering theory

KW - Second law of thermodynamics

KW - Seebeck effect

KW - Stochastic thermodynamics

KW - Thermal conductance

KW - Thermoelectric figure of merit

KW - Thermoelectricity

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U2 - 10.1016/j.physrep.2017.05.008

DO - 10.1016/j.physrep.2017.05.008

M3 - Review article

AN - SCOPUS:85054365502

VL - 694

SP - 1

EP - 124

JO - Physics Reports

JF - Physics Reports

SN - 0370-1573

ER -