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Register a new userThermodynamic uncertainty relation in quantum thermoelectric junctions
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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.
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The thermodynamic uncertainty relation (TUR) is expected to hold in nanoscale electronic conductors, when the electron transport process is quantum coherent and the transmission probability is constant (energy and voltage independent). We present measurements of the electron current and its noise in gold atomic-scale junctions and confirm the validity of the TUR for electron transport in realistic quantum coherent conductors. Furthermore, we show that it is beneficial to present the current and its noise as a TUR ratio in order to identify deviations from noninteracting-electron coherent dynamics.
To reveal the role of the quantumness in the Otto cycle and to discuss the validity of the thermodynamic uncertainty relation (TUR) in the cycle, we study the quantum Otto cycle and its classical counterpart. In particular, we calculate exactly the mean values and relative error of thermodynamic quantities. In the quasistatic limit, quantumness reduces the productivity and precision of the Otto cycle compared to that in the absence of quantumness, whereas in the finite-time mode, it can increase the cycles productivity and precision. Interestingly, as the strength (heat conductance) between the system and the bath increases, the precision of the quantum Otto cycle overtakes that of the classical one. Testing the conventional TUR of the Otto cycle, in the region where the entropy production is large enough, we find a tighter bound than that of the conventional TUR. However, in the finite-time mode, both quantum and classical Otto cycles violate the conventional TUR in the region where the entropy production is small. This implies that another modified TUR is required to cover the finite-time Otto cycle. Finally, we discuss the possible origin of this violation in terms of the uncertainty products of the thermodynamic quantities and the relative error near resonance conditions.
A duality relation between the long-time dynamics of a quantum Brownian particle in a tilted ratchet potential and a driven dissipative tight-binding model is reported. It relates a situation of weak dissipation in one model to strong dissipation in the other one, and vice versa. We apply this duality relation to investigate transport and rectification in ratchet potentials: From the linear mobility we infer ground-state delocalization for weak dissipation. We report reversals induced by adiabatic driving and temperature in the ratchet current and its dependence on the potential shape.
Thermodynamic equilibrium properties of a macroscopic system emerge from an interaction with a thermal bath. In the weak coupling regime, the description of thermodynamic states turns possible to describe the system in terms of its time-independent intensive and extensive variables. However, this is not an obvious task in both the classical and quantum cases when either dealing with finite systems described by a few degrees of freedom when the statistical fluctuations play an important role, i.e., not in the thermodynamic limit, or the coupling between the system and the environment is of the same order of magnitude as their energies. On the other hand, in recent years, metrology has been extended to the quantum regime in such a way that the fluctuation of physical quantities plays a crucial role in the precise estimation of parameters. Using metrology tools, it is possible to derive an uncertainty relation between the internal energy and temperature of systems for arbitrary linear coupling scales, showing an important connection between the two research fields. Our work is dedicated to the generalization of the thermodynamic uncertainty relations between an intensive and an extensive quantity for all coupling regimes in the quantum scenario through the generalized Gibbs ensemble (GGE). First, we demonstrate a fundamental limit between the intensive and extensive quantity for a total GGE state, which makes it possible to take the trace of the degrees of freedom of one of the systems and evaluate the uncertainty relation in the system of interest. After that, we performed a series of examples to corroborate the results already existing in the literature, thus showing the versatility of our method.
We provide a thermodynamically consistent description of energy, charge and spin transfers in a thermoelectric quantum-dot spin valve in the collinear configuration based on nonequilibrium Greens function and full counting statistics. We use the fluctuation theorem symmetry and the concept of entropy production to characterize the efficiency with which thermal gradients can transduce charges or spins against their chemical potentials, arbitrary far from equilibrium. Close to equilibrium, we recover the Onsager reciprocal relations and the connection to linear response notions of performance such as the figure of merit. We also identify regimes where work extraction is more efficient far then close from equilibrium.
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