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Register a new userGeneralized uncertainty relation between thermodynamic variables in quantum thermodynamics
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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.
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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.
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 relation is found between pulsed measurements of the excited state probability of a two-level atom illuminated by a driving laser, and a continuous measurement by a second laser coupling the excited state to a third state which decays rapidly and irreversibly. We find the time between pulses to achieve the same average detection time than a given continuous measurement in strong, weak, or intermediate coupling regimes, generalizing the results in L. S. Schulman, Phys. Rev. A 57, 1509 (1998).
Uncertainty relation is one of the fundamental principle in quantum mechanics and plays an important role in quantum information science. We experimentally test the error-disturbance uncertainty relation (EDR) with continuous variables for Gaussian states. Two conjugate continuous-variable observables, amplitude and phase quadratures of an optical mode, are measured simultaneously by using a heterodyne measurement system. The EDR with continuous variables for a coherent state, a squeezed state and a thermal state are verified experimentally. Our experimental results demonstrate that Heisenbergs EDR with continuous variables is violated, yet Ozawas and Branciards EDR with continuous variables are validated.
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