• Open Access

Stochastic and Quantum Thermodynamics of Driven RLC Networks

Nahuel Freitas, Jean-Charles Delvenne, and Massimiliano Esposito
Phys. Rev. X 10, 031005 – Published 7 July 2020

Abstract

We develop a general stochastic thermodynamics of RLC electrical networks built on top of a graph-theoretical representation of the dynamics commonly used by engineers. The network is (i) open, as it contains resistors and current and voltage sources, (ii) nonisothermal, as resistors may be at different temperatures, and (iii) driven, as circuit elements may be subjected to external parametric driving. The proper description of the heat dissipated in each resistor requires care within the white-noise idealization as it depends on the network topology. Our theory provides the basis to design circuits-based thermal machines, as we illustrate by designing a refrigerator using a simple driven circuit. We also derive exact results for the low-temperature regime in which the quantum nature of the electrical noise must be taken into account. We do so using a semiclassical approach, which can be shown to coincide with a fully quantum treatment of linear circuits for which canonical quantization is possible. We use this approach to generalize the Landauer-Büttiker formula for energy currents to arbitrary time-dependent driving protocols.

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  • Received 13 August 2019
  • Revised 18 February 2020
  • Accepted 6 May 2020

DOI:https://doi.org/10.1103/PhysRevX.10.031005

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsGeneral PhysicsQuantum Information, Science & TechnologyNetworks

Authors & Affiliations

Nahuel Freitas1, Jean-Charles Delvenne2, and Massimiliano Esposito1

  • 1Complex Systems and Statistical Mechanics, Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
  • 2Institute of Information and Communication Technologies, Electronics and Applied Mathematics, Université catholique de Louvain, Louvain-La-Neuve, Belgium

Popular Summary

The miniaturization of electronics over the last decades has been spectacular. Nowadays, electronic circuits can operate far from equilibrium at scales where thermal fluctuations cannot be neglected anymore. At very low temperature, they even operate in the quantum regime. Surprisingly, a systematic theory describing heat flows in even the simplest class of circuits, the RLC circuits, has still been missing. We establish such a theory in the classical and quantum regime and show how to use it to design circuit-based thermodynamic machines capable of controlling heat and charge flows across the circuits.

The theory starts from a “graph-theoretical representation” of RLC circuits developed by engineers in the 1960s. It then makes use of recent developments in stochastic and quantum thermodynamics to incorporate thermal noises in the equations of motion for the capacitor charges and the inductance currents.

A key finding is that only some circuit topologies, which we characterize, ensure that this procedure generates correct heat flows, ruling out some thermodynamically inconsistent simplifying assumptions commonly used by practitioners. Another finding is that the very-low-temperature regime of our theory is dominated by quantum effects that cannot be captured within traditional theories and also ensure the validity of the third law of thermodynamics.

Reducing energy consumption, preventing overheating, and designing quantum computers are all major concerns for information technologies. By establishing the theory describing the thermodynamics of simple circuits, our work provides new important tools toward addressing those concerns.

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Vol. 10, Iss. 3 — July - September 2020

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