### Abstract

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?

Original language | English |
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Journal | Physics Reports |

DOIs | |

Publication status | Accepted/In press - 2017 |

### Fingerprint

### Keywords

- Andreev reflection
- Dynamical quantum systems
- Entropy production
- Finite-time thermodynamics
- Linear response
- Master equations
- Non-equilibrium thermodynamics
- Onsager relations
- Peltier cooling
- Quantum dots
- Quantum Hall effect
- Quantum point contacts
- Quantum thermodynamics
- Quantum transport
- Scattering theory
- Second law of thermodynamics
- Seebeck effect
- Stochastic thermodynamics
- Thermal conductance
- Thermoelectric figure of merit
- Thermoelectricity

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Reports*. https://doi.org/10.1016/j.physrep.2017.05.008

**Fundamental aspects of steady-state conversion of heat to work at the nanoscale.** / Benenti, Giuliano; Casati, Giulio; Saito, Keiji; Whitney, Robert S.

Research output: Contribution to journal › Article

*Physics Reports*. https://doi.org/10.1016/j.physrep.2017.05.008

}

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.

PY - 2017

Y1 - 2017

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. 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?

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. 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?

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 dots

KW - Quantum Hall effect

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 - Article

JO - Physics Reports

JF - Physics Reports

SN - 0370-1573

ER -