Fundamental aspects of steady-state conversion of heat to work at the nanoscale
Résumé
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. 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) master 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?