Universal Bounds on Fluctuations in Continuous Thermal Machines

Abstract

We study bounds on ratios of fluctuations in steady-state time-reversal heat engines controlled by multi affinities. In the linear response regime, we prove that the relative fluctuations (precision) of the output current (power) is always lower-bounded by the relative fluctuations of the input current (heat current absorbed from the hot bath). As a consequence, the ratio between the fluctuations of the output and input currents are bounded both from above and below, where the lower (upper) bound is determined by the square of the averaged efficiency (square of the Carnot efficiency) of the engine. The saturation of the lower bound is achieved in the tight-coupling limit when the determinant of the Onsager response matrix vanishes. Our analysis can be applied to different operational regimes, including engines, refrigerators, and heat pumps. We illustrate our findings in two types of continuous engines: two-terminal coherent thermoelectric junctions and three-terminal quantum absorption refrigerators. Numerical simulations in the far-from-equilibrium regime suggest that these bounds apply more broadly, beyond linear response.

Quantum transport in quasi-periodic lattice systems in presence of Büttiker probes

“…We next move on to analyze two recently obtained universal bounds [54,55] for the mean efficiency in the context of our thermoelectric engines. Interestingly, these universal bounds are found to be tighter than the seminal Carnot bound and are written in terms of the current fluctuations.…”

“…Very recently, another tighter bound on engine's efficiency was obtained in Ref. [54,65] by idenfying the input and output currents and imposing conditions on the direction of these current such that the thermoelectric setup operates as an engine. This bound, in our context translates to…”

“…We also investigated the thermoelectric properties of the AAH model by incorporating voltage-temperature probes and further assessed, in presence of probes, the validity of two recently obtained tighter bounds on thermoelectric engine efficiency and also showed that the bound obtained following Ref. [54] is always tighter than the one predicted by the TUR.…”

“…We implement both the voltage probe and voltagetemperature probe techniques and explore charge transport and thermoelectric heat-to-work conversion properties in the linear-response regime. For the thermoelectric setup, we further asses and compare the recently obtained tighter bounds on efficiency following the thermodynamic uncertainty relations [54] and the bound obtained in Ref. [55].…”

Geometric thermodynamic uncertainty relation in periodically driven thermoelectric heat engine

“…It is known that the TUR was initially proposed in the long-time limit [9,24] and later generalized to the finitetime dynamics [25]. Consequently, the analysis methods and corresponding physical implications are further refined [26][27][28]. Although TUR has been widely applied in tremendous amount of systems, it is not always valid.…”