Efficiency fluctuations in quantum thermoelectric devices

Esposito, Massimiliano; Ochoa, Maicol A.; Galperin, Michael

doi:10.48550/arxiv.1501.03232

Cited by 3 publications

(4 citation statements)

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“…5 b). Furthermore, one observes that its maximum (along the dashed vertical line) lies at the Carnot efficiency (η C = 0.6) in agreement with previous results [41,63,64,42,65]. The Carnot efficiency is thus the least likely to be observed in the long time limit.…”

Section: Regime Of Thermoelectric Conversionsupporting

confidence: 90%

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Double quantum dot coupled to a quantum point contact: a stochastic thermodynamics approach

Cuetara

Esposito

2015

New J. Phys.

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We study the nonequilibrium properties of an electronic circuit composed of a double quantum dot (DQD) channel capacitively coupled to a quantum point contact (QPC) within the framework of stochastic thermodynamics. We show that the transition rates describing the dynamics satisfy a nontrivial local detailed balance and that the statistics of energy and particle currents across both channels obeys a fluctuation theorem. We analyze two regimes where the device operates as a thermodynamic machine and study its output power and efficiency fluctuations. We show that the electrons tunneling through the QPC without interacting with the DQD have a strong effect on the device efficiency.The microscopic processes underlying such transitions involve the tunneling of an electron between the QPC reservoirs which exchanges a fraction of its energy with the DQD. As a result, the transition rates cannot be written anymore as a sum where each term only involves one single reservoir. Despite this non additivity of the rates, the local detailed balance (LDB) [37, 39] is shown to hold, and is explicitly written in terms of the fluxes of entropy from the reservoirs involved in the transitions.Furthermore, since some electrons tunnel between the QPC reservoirs without exchanging energy with the DQD, they do not induce transitions in the DQD but need to be taken into account in the counting statistics. We show that their statistics is well described by the modified quantum master equation and corresponds to the Levitov-Lesovik formula [40-44] to second order perturbation theory in the coupling between the QPC reservoirs. Though such processes do not reveal themselves in the master equation for the DQD populations, they are shown to strongly impact the circuit performance.We proceed by analyzing two different regimes where the circuit operates as a thermoelectric and as a current converter, respectively. We identify the optimal working conditions to reach large average output power and high macroscopic efficiency and study the statistical properties of the output power as well as of the efficiency, as recently proposed in [45][46][47].The paper is organized as follows: the model is introduced in section 2. In section 3, we derive the modified quantum master equation to calculate the counting statistics of energy and matter currents, and analyze the microscopic processes contributing to the transition rates. In section 4, using the LDB property of the rates, we identify the entropy flows associated to each microscopic processes in the circuit, and the steady state FT is derived. The expressions for the average energy and matter currents as well as the average irreversible entropy production are also provided. The thermodynamic analysis of the circuit operating as a thermoelectric and as a current converter is done in section 5. Conclusions are drawn in section 6. +--+ From these expressions, one readily verifies the conservation laws J J J J J J J 0, and . 69

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Section: Regime Of Thermoelectric Conversionsupporting

confidence: 90%

“…exhibits universal properties [41,63,64,42,65,66]. We now briefly show that the FCS of the currents developed in Sec.…”

Section: Regime Of Thermoelectric Conversionmentioning

confidence: 79%

Double quantum dot coupled to a quantum point contact: a stochastic thermodynamics approach

Cuetara

Esposito

2015

New J. Phys.

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“…The non self-averaging nature of fluctuations in stochastic efficiency and other quantities requires detailed understanding of full probability distributions as opposed to the average behavior [41,42]. Large deviation properties of such distributions are recently under theoretical investigations [45,46,47,48,49,50,51]. Research on fluctuation relations for heat engines [52,53,54] are being pursued.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Brownian refrigerator

Rana

Pal

Saha

et al. 2016

Physica A: Statistical Mechanics and its Applications

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We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the system cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on the bath temperatures. Interestingly, in non-quasistatic regime, our system can even work as a stochastic heat engine for certain range of cycle time and bath temperatures. We show that the operation of this engine is not reliable. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values. Their distributions show power law tails, however the exponents are not universal. Our study reveals that microscopic machines are not the microscopic equivalent of the macroscopic machines that we come across in our daily life. We find that there is no one to one correspondence between the performance of our system under engine protocol and its reverse.

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“…The theorem was actually first derived in this context [31,32,33,34]. Surprisingly, the impact of these new insights on the efficiency, and in particular on its stochastic properties, has only been considered very recently [35,36,37,38,39,40,41,42,43],…”

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confidence: 99%

Stochastic efficiency: five case studies

Proesmans

Broeck

2015

New J. Phys.

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Stochastic efficiency is evaluated in five case studies: driven Brownian motion, effusion with a thermochemical and thermo-velocity gradient, a quantum dot and a model for information to work conversion. The salient features of stochastic efficiency, including the maximum of the large deviation function at the reversible efficiency, are reproduced. The approach to and extrapolation into the asymptotic time regime are documented.

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Efficiency fluctuations in quantum thermoelectric devices

Cited by 3 publications

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Double quantum dot coupled to a quantum point contact: a stochastic thermodynamics approach

Double quantum dot coupled to a quantum point contact: a stochastic thermodynamics approach

Anomalous Brownian refrigerator

Stochastic efficiency: five case studies

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