Thermodynamic uncertainty relation in quantum thermoelectric junctions

Abstract

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]

Thermodynamic uncertainty relation in thermal transport

“…In Ref. 24 , we further examined the validity of the TUR in thermoelectric junctions of noninteracting electrons, and analyzed the related power-efficiency-power fluctuation trade-off relation.…”

Strong coupling in thermoelectric nanojunctions: a reaction coordinate framework

“…We now extend our analysis to consider higher cumulants, specifically the zero frequency noise I 2 , and potential trade-offs between fluctuations and the thermoelectric power and efficiency. We are motivated in part by recent advances in the study of thermodynamic uncertainty relations (TURs) [39][40][41][42][43][44][45][46]. Steady-state TURs provide cost-precision trade-off relations whereby the relative uncertainty in the current…”

“…The system thus generates a finite power output with an associated efficiency, determined also by the heat flux. We are particularly interested in understanding the interplay between the power, efficiency, and noise, which is of key importance in assessing the performance of thermodynamic devices [39][40][41][42][43][44][45][46].…”

Geometric thermodynamic uncertainty relation in periodically driven thermoelectric heat engine

“…Recently, a thermodynamic uncertainty relation (TUR) has been formulated based on classical Markovian steady states, which demonstrates the trade-off relation between relative current fluctuation and dissipation [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Specifically, the average current I , its variance I 2 ≡ (I − I ) 2 , and the entropy production rate σ is universally bounded as…”