Estimating the efficiency of Brazilian electricity distribution utilities.

This paper proposes a differing methodology from the Brazilian Electricity Regulatory Agency on the efficiency estimation for the Brazilian electricity distribution sector. Our proposal combines robust state-space models and stochastic frontier analysis to measure the operational cost efficiency in a panel data set from 60 Brazilian electricity distribution utilities. The modeling joins the main literature in energy economics with advanced econometric and statistic techniques in order to estimate the efficiencies. Moreover, the suggested model is able to deal with changes in the inefficiencies across time whilst the Bayesian paradigm - through Markov chain Monte Carlo techniques - facilitates the inference on all unknowns. The method enables a significant degree of flexibility in the resultant efficiencies and a complete photography about the distribution sector.

Unifying Paradigms of Quantum Refrigeration: A Universal and Attainable Bound on Cooling.

Cooling quantum systems is arguably one of the most important thermodynamic tasks connected to modern quantum technologies and an interesting question from a foundational perspective. It is thus of no surprise that many different theoretical cooling schemes have been proposed, differing in the assumed control paradigm and complexity, and operating either in a single cycle or in steady state limits. Working out bounds on quantum cooling has since been a highly context dependent task with multiple answers, with no general result that holds independent of assumptions. In this Letter we derive a universal bound for cooling quantum systems in the limit of infinite cycles (or steady state regimes) that is valid for any control paradigm and machine size. The bound only depends on a single parameter of the refrigerator and is theoretically attainable in all control paradigms. For qubit targets we prove that this bound is achievable in a single cycle and by autonomous machines.

Unifying paradigms of quantum refrigeration: Fundamental limits of cooling and associated work costs.

In classical thermodynamics the work cost of control can typically be neglected. On the contrary, in quantum thermodynamics the cost of control constitutes a fundamental contribution to the total work cost. Here, focusing on quantum refrigeration, we investigate how the level of control determines the fundamental limits to cooling and how much work is expended in the corresponding process. We compare two extremal levels of control: first, coherent operations, where the entropy of the resource is left unchanged, and, second, incoherent operations, where only energy at maximum entropy (i.e., heat) is extracted from the resource. For minimal machines, we find that the lowest achievable temperature and associated work cost depend strongly on the type of control, in both single-cycle and asymptotic regimes. We also extend our analysis to general machines. Our work provides a unified picture of the different approaches to quantum refrigeration developed in the literature, including algorithmic cooling, autonomous quantum refrigerators, and the resource theory of quantum thermodynamics.

Autonomous thermal machine for amplification and control of energetic coherence.

We present a model for an autonomous quantum thermal machine composed of two qubits capable of manipulating and even amplifying the local coherence in a nondegenerate external system. The machine uses only thermal resources, namely, contact with two heat baths at different temperatures, and the external system has a nonzero initial amount of coherence. The method we propose allows for an interconversion between energy, both work and heat, and coherence in an autonomous configuration working in out-of-equilibrium conditions. This model raises interesting questions about the role of fundamental limitations on transformations involving coherence and opens up new possibilities in the manipulation of coherence by autonomous thermal machines.

Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamical resource.

Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship between the size of the machine (captured by Hilbert space dimension) and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: Reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.

Thermodynamics of quantum systems with multiple conserved quantities.

Recently, there has been much progress in understanding the thermodynamics of quantum systems, even for small individual systems. Most of this work has focused on the standard case where energy is the only conserved quantity. Here we consider a generalization of this work to deal with multiple conserved quantities. Each conserved quantity, which, importantly, need not commute with the rest, can be extracted and stored in its own battery. Unlike the standard case, in which the amount of extractable energy is constrained, here there is no limit on how much of any individual conserved quantity can be extracted. However, other conserved quantities must be supplied, and the second law constrains the combination of extractable quantities and the trade-offs between them. We present explicit protocols that allow us to perform arbitrarily good trade-offs and extract arbitrarily good combinations of conserved quantities from individual quantum systems.

Small quantum absorption refrigerator with reversed couplings.

Small quantum absorption refrigerators have recently attracted renewed attention. Here we present a missing design of a two-qubit fridge, the main feature of which is that one of the two machine qubits is itself maintained at a temperature colder than the cold bath. This is achieved by "reversing" the couplings to the baths compared to previous designs, where only a transition is maintained cold. We characterize the working regime and the efficiency of the fridge. We demonstrate the soundness of the model by deriving and solving a master equation. Finally, we discuss the performance of the fridge, in particular the heat current extracted from the cold bath. We show that our model performs comparably to the standard three-level quantum fridge and thus appears appealing for possible implementations of nanoscale thermal machines.

Multiple Observers Can Share the Nonlocality of Half of an Entangled Pair by Using Optimal Weak Measurements.

We investigate the trade-off between information gain and disturbance for von Neumann measurements on spin-1/2 particles, and derive the measurement pointer state that saturates this trade-off, which turns out to be highly unusual. We apply this result to the question of whether the nonlocality of a single particle from an entangled pair can be shared among multiple observers that act sequentially and independently of each other, and show that an arbitrarily long sequence of such observers can all violate the Clauser-Horne-Shimony-Holt-Bell inequality.

Passivity, complete passivity, and virtual temperatures.

We give a simple and intuitive proof that the only states which are completely passive, i.e., those states from which work cannot be extracted even with infinitely many copies, are Gibbs states at positive temperatures. The proof makes use of the idea of virtual temperatures, i.e., the association of temperatures to pairs of energy levels (transitions). We show that (1) passive states are those where every transition is at a positive temperature and (2) completely passive states are those where every transition is at the same positive temperature.

Entanglement enhances cooling in microscopic quantum refrigerators.

Small self-contained quantum thermal machines function without external source of work or control but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned-fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence, a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.