Mapping of uncertainty relations between continuous and discrete time

Chiuchiù, Davide; Pigolotti, Simone

doi:10.1103/physreve.97.032109

Cited by 43 publications

(67 citation statements)

References 27 publications

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“…We set d = 0, such that T 1 1 = d T 0 1 = 0 in Eq. (14). In particular in the resonant tunnelling regime we require that f L <f R as currents should be negative, or equivalently,…”

Section: B Thermoelectric Enginesmentioning

confidence: 99%

Thermodynamic uncertainty relation in quantum thermoelectric junctions

Liu

Segal

2019

Phys. Rev. E

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Recently, a thermodynamic uncertainty relation (TUR) has been formulated for classical Markovian systems demonstrating trade-off between precision (current fluctuation) and cost (dissipation). Systems that violate the TUR are interesting as they overcome another trade-off relation concerning the efficiency of a heat engine, its power, and its stability (power fluctuations). Here, we analyze the root, extent, and impact on performance of TUR violations in quantum thermoelectric junctions at steady state. Considering noninteracting electrons, first we show that only the "classical" component of the current noise, arising from single-electron transfer events follows the TUR. The remaining, "quantum" part of current noise is therefore responsible for the potential violation of TUR in such quantum systems. Next, focusing on the resonant transport regime we determine the parameter range in which the violation of the TUR can be observed-for both voltage-biased junctions and thermoelectric engines. We illustrate our findings with exact numerical simulations of a serial double quantum dot system. Most significantly, we demonstrate that the TUR always holds in noninteracting thermoelectric generators when approaching the thermodynamic efficiency limit. arXiv:1904.11963v1 [cond-mat.mes-hall]

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“…We set d = 0, such that T 1 1 = d T 0 1 = 0 in Eq. (14). In particular in the resonant tunnelling regime we require that f L <f R as currents should be negative, or equivalently,…”

Section: B Thermoelectric Enginesmentioning

confidence: 99%

Thermodynamic uncertainty relation in quantum thermoelectric junctions

Liu

Segal

2019

Phys. Rev. E

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“…A key feature of this parabolic bound is that it depends solely on the average entropy production and the average current, i.e., knowledge of the average entropy production and the average current implies a bound on arbitrary fluctuations of any thermodynamic current. There has been much recent work related to this universal principle about current fluctuations [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Bounds on current fluctuations in periodically driven systems

et al. 2018

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Small nonequilibrium systems in contact with a heat bath can be analyzed with the framework of stochastic thermodynamics. In such systems, fluctuations, which are not negligible, follow universal relations such as the fluctuation theorem. More recently, it has been found that, for nonequilibrium stationary states, the full spectrum of fluctuations of any thermodynamic current is bounded by the average rate of entropy production and the average current. However, this bound does not apply to periodically driven systems, such as heat engines driven by periodic variation of the temperature and artificial molecular pumps driven by an external protocol. We obtain a universal bound on current fluctuations for periodically driven systems. This bound is a generalization of the known bound for stationary states. In general, the average rate that bounds fluctuations in periodically driven systems is different from the rate of entropy production. We also obtain a local bound on fluctuations that leads to a trade-off relation between speed and precision in periodically driven systems, which constitutes a generalization to periodically driven systems of the so called thermodynamic uncertainty relation. From a technical perspective, our results are obtained with the use of a recently developed theory for 2.5 large deviations for Markov jump processes with time-periodic transition rates.

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“…Later, Proesmans et al [33] obtained the thermodynamic uncertainty relation for the discrete time Markov chain using the large deviation techniques. A connection between discrete and continuous time uncertainty relations is shown in [34]. One can also see similar uncertainty relations in the context of discrete processes [35], multidimensional systems [36], Brownian motion in the tilted periodic potential [37], general Langevin systems [38], molecular motors [39], run and tumble processes [40], biochemical oscillations [41], interacting oscillators [42], effect of magnetic field [43], linear response [44], measurement and feedback control [45], information [46], underdamped Langevin dynamics [47], timedelayed Langevin systems [48], various systems [49], etc..…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic uncertainty relations in a linear system

Gupta

Maritan

2020

Eur. Phys. J. B

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We consider a Brownian particle in harmonic confinement of stiffness k, in one dimension in the underdamped regime. The whole setup is immersed in a heat bath at temperature T . The center of harmonic trap is dragged under any arbitrary protocol. The thermodynamic uncertainty relations for both position of the particle and current at time t are obtained using the second law of thermodynamics as well as the positive semi-definite property of the correlation matrix of work and degrees of freedom of the system for both underdamped and overdamped cases. arXiv:1905.08854v2 [cond-mat.stat-mech]

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Mapping of uncertainty relations between continuous and discrete time

Cited by 43 publications

References 27 publications

Thermodynamic uncertainty relation in quantum thermoelectric junctions

Thermodynamic uncertainty relation in quantum thermoelectric junctions

Bounds on current fluctuations in periodically driven systems

Thermodynamic uncertainty relations in a linear system

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