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Demand response is a concept that has been around since the very first electric power systems. However, we have seen an explosion of research on demand response and demand-side technologies in the past 30 years, coinciding with the shift towards liberalized/deregulated electricity markets and efforts to decarbonize the power sector. Now we are also seeing a shift towards more distributed/decentralized electric systems; we have entered the era of "distributed energy resources," which require new grid management, operational, and control strategies. Given this paradigm shift, we argue that the concept of demand response needs to be revisited, and more carefully/consistently defined to enable us to better utilize this massive resource for economic, technical, environmental, and societal aims. In this paper, we survey existing demand response definitions, highlight their shortcomings, propose a new definition, and describe how this new definition enables us to more effectively harness the value of demand response in modern power systems. We conclude with a demand response research agenda informed by a discussion of demand response barriers and enablers., Comment: 12 pages

We introduce and explore the notion of texture of an arbitrary quantum state, in a selected basis. In the first part of this letter we develop a resource theory and show that state texture is adequately described by an easily computable monotone, which is also directly measurable. It is shown that textures are useful in the characterization of unknown quantum gates in universal circuit layers. By using randomized input states and recording the textures of the output qubits we are able to fully characterize the circuit layer, whenever it contains at least one CNOT gate. This can be done without the need of tomographic protocols and the use of ancillary systems., Comment: To appear on Phys. Rev. Lett

In this paper, we address distributed Time-Varying Resource Allocation (TVRA) problem, where the local cost functions, global equality constraint, and Local Feasibility Constraints (LFCs) vary with time. To track the optimal trajectories, algorithms that mimic the structure of feedback-feedforward control systems are proposed. We begin with their conceptual design in the absence of LFCs, developing a feedback-feedforward algorithm that is fixed-time convergent. For cases with LFCs, existing approaches predominantly rely on constructing a time-dependent barrier function, which may impede the design of fixed-time convergent algorithms. Therefore, by exploring the connection between projection and penalty functions, switched feedforward laws are tailored to handle LFCs, with projection used in conjunction. Based on this, we develop a projection-based feedback-feedforward algorithm, which converges to the exact optimal trajectories, possibly along with a number of switching instants, while exhibiting fixed-time convergence between consecutive switching instants. Numerical experiments verify the effectiveness of the proposed algorithms.

We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions. Since the Hamiltonians also contain deterministic one-body terms, by varying the interaction strength, one can continuously interpolate between deterministic separable eigenstates and fully random entangled eigenstates, with non-trivial intermediate behavior. Entanglement strongly depends on the underlying topology of the interaction among the qubits. For a certain class of interactions GHZ entanglement is favoured by a non-separable collective interaction, while for fully separable pairwise interactions the ground states concentrate in the vicinity of W states.

Taking advantage of the fact that the cardinalities of hidden variables in network scenarios can be assumed to be finite without loss of generality, a numerical tool for finding explicit local models that reproduce a given statistical behaviour was developed. The numerical procedure was then validated using families of statistical behaviours for which the network-local boundary is known, in the bilocal scenario. Furthermore, the critical visibility for 3 notable distributions mixed with a uniform random noise is investigated in the triangle network without inputs. We provide conjectures for the critical visibilities of the Greenberger-Horne-Zeilinger (GHZ) and W distributions (which are roots of 4th degree polynomials), as well as a lower bound estimate of the critical visibility of the Elegant Joint Measurement distribution. The developed codes and documentation are publicly available at github.com/mariofilho281/localmodels, Comment: 10 pages and 8 figures. Updated to match the published version

The global trend toward renewable power generation has drawn great attention to hydrogen Fuel Cells (FCs), which have a wide variety of applications, from utility power stations to laptops. The Multi-stack Fuel Cell System (MFCS), which is an assembly of FC stacks, can be a remedy for obstacles in high-power applications. However, the output voltage of FC stacks varies dramatically under variable load conditions; hence, in order for MFCS to be efficiently operated and guarantee an appropriate load-current sharing among the FC stacks, advanced converter controllers for power conditioning need to be designed. An accurate circuit model is essential for controller design, which accounts for the fact that the parameters of some converter components may change due to aging and repetitive stress in long-term operations. Existing control frameworks and parametric and non-parametric system identification techniques do not consider the aforementioned challenges. Thus, this paper investigates the potential of a data-driven method that, without system identification, directly implements control on paralleled converters using raw data. Based on pre-collected input/output trajectories, a non-parametric representation of the overall circuit is produced for implementing predictive control. While approaching equal current sharing within the MFCS, the proposed method considers the minimization of load-following error and mitigation of circulating current between the converters. Simulation results verify the effectiveness of the proposed method.

Whenever a physical quantity becomes essential to the realization of useful tasks, it is desirable to define proper measures or monotones to quantify it. In quantum mechanics, coherence, entanglement, and Bell nonlocality are examples of such quantities. Given a quantum state $\varrho$ and a quantifier ${\cal E}(\varrho)$, both arbitrary, it is a hard task to determine ${\cal E}(\varrho^{\otimes N})$. However, if the figure of merit $\cal{E}$ turns out to be additive, we simply have ${\cal E}(\varrho^{\otimes N})=N e$, with $e={\cal E}(\varrho)$. In this work we generalize this useful notion through the inner product ${\cal E}(\varrho^{\otimes N}) = \vec{N}\cdot \vec{e}$, where $\vec{e}=({\cal E}(\varrho^{\otimes i_1}), {\cal E}(\varrho^{\otimes i_2}),\dots,{\cal E}(\varrho^{\otimes i_q}) )$ is a vector whose $q$ entries are the figure of merit under study calculated for some numbers of copies smaller than $N$ ($1 \le i_1

This paper presents a novel scheme termed Optimization-based Ramping Reserve Allocation (ORRA) for addressing an ongoing challenge in Automatic Generation Control (AGC) enhancement, i.e., the optimal coordination of multiple Battery Energy Storage Systems (BESSs). While exploiting further the synergy between BESSs and slow ramping resources, the proposed scheme offers an insight into the energy-neutral operation, which is achieved by smoothly discontinuing the BESS participation along with the minimization of Area Injection Error (AIE), a variant of traditional Area Control Error (ACE). The first stage of ORRA is to incorporate Neural Networks (NNs) with the AIE in order to ensure a zero-mean of ramping reserves to be allocated among BESSs. These AIE signals are then used to formulate the optimal coordination of BESS as an online optimization problem, which is therefore feedback-driven. Finally, a distributed optimization algorithm is developed to solve the formulated problem in real-time, achieving a sublinear dynamic regret that quantifies the cost difference to the trajectory computed by a centralized optimizer with perfect global information. Consistent with the geographical distribution of BESSs, the proposed ORRA is fully distributed such that the algorithm can be executed in parallel at all nodes. Simulations on a modified IEEE 14-bus system are performed to illustrate the effectiveness and important features of ORRA.

We define an alternative way of quantifying nonlocality of states based on Bell nonlocality of behaviors, called the trace-weighted nonlocal volume. The construction is based on the nonlocal volume, a quantifier of nonlocality for states that counts the volume of the set of measurements that give rise to nonlocal behaviors when applied to this state, plus the trace distance, a quantifier of nonlocality for behaviors based on the distance between the behavior and the local set. The key difference from preceding candidates was the introduction of a quantifier of nonlocality to weight each contribution from behaviors in the nonlocal volume. We list some interesting properties of this quantifier and investigate the (2, 2, 2) and (2, 3, 2) scenarios. We show that the weak anomaly of nonlocality for the (2, 2, 3) scenario persists, but the local minimum for nonlocality with the trace-weighted nonlocal volume occurs in a different state as compared to the minimum for the non-weighted version, showing that the weak anomaly is not an intrinsic characteristic of the scenario, but is dependent of the choice of quantifier., Comment: 12 pages, 11 figures

We present a kicked harmonic oscillator where the impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom and not by the canonical quantization of a time-dependent Hamiltonian. The ancila is dynamically entangled with the oscillator position, while the background Hamiltonian remains static. The dynamics of this system is determined in closed analytical form, allowing for the evaluation of a properly defined Loschmidt echo, ensemble averages, and phase-space portraits. As in the case of standard Floquet systems we observe regimes with crystalline and quasicrystalline structures in phase space, resonances, and evidences of chaotic behavior, however, not originating from any classically chaotic system.

Given an arbitrary state $\rho$ and some figure of merit ${\cal E}(\rho)$, it is usually a hard problem to determine the value of ${\cal E}(\rho^{\otimes N})$. One noticeable exception is the case of additive measures, for which we simply have ${\cal E}(\rho^{\otimes N}) = Ne$, with $e\equiv {\cal E}(\rho)$. In this work we study measures that can be described by ${\cal E}(\rho^{\otimes N}) =E(e;N) \ne Ne$, that is, measures for which the amount of resources of $N$ copies is still determined by the single real variable $e$, but in a nonlinear way. If, in addition, the measures are analytic around $e=0$, recurrence relations can be found for the Maclaurin coefficients of $E$ for larger $N$. As an example, we show that the $\ell_1$-norm of coherence is a nontrivial case of such a behavior.

A "circular orbital forcing" makes a chosen point on a rigid body follow a circular motion while the body spins freely around that point. We investigate this problem for the planar motion of a body subject to dry friction. We focus on the effect called reverse rotation (RR), where spinning and orbital rotations are antiparallel. Similar reverse dynamics include the rotations of Venus and Uranus, journal machinery bearings, tissue production reactors, and chiral active particles. Due to dissipation, RRs are possible only as a transient. Here the transient or flip time $t_\textrm{f}$ depends on the circular driving frequency $\omega$, unlike the viscous case previously studied. We find $t_\textrm{f}\sim\omega^{\gamma-1}\mu^{-\gamma/2}$, where $\mu$ is the friction coefficient and $\gamma=0$ ($\gamma=2$) for low (high) $\omega$. Whether RRs really occur depends on the initial conditions as well as on $\mu$ and $H$, a geometrical parameter. The critical $H_\textrm{c}(\mu)$ where RRs become possible follows a $q$-exponential with $q\simeq1.9$, a more restrictive RR scenario than in the wet case. We use animations to visualize the different dynamical regimes that emerge from the highly nonlinear dissipation mechanism of dry friction. Our results are valid across multiple investigated rigid body shapes., Comment: 11 pages, 10 figures

The canonical operator $\hat{a}^{\dagger}$ ($\hat{a}$) represents the ideal process of adding (subtracting) an {\it exact} amount of energy $E$ to (from) a physical system in both elementary quantum mechanics and quantum field theory. This is a ``sharp'' notion in the sense that no variability around $E$ is possible at the operator level. In this work, we present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons., Comment: arXiv admin note: text overlap with arXiv:1905.08206 Close to the published version

The question of how quantities, like entanglement and coherence, depend on the number of copies of a given state $\rho$ is addressed. This is a hard problem, often involving optimizations over Hilbert spaces of large dimensions. Here, we propose a way to circumvent the direct evaluation of such quantities, provided that the employed measures satisfy a self-similarity property. We say that a quantity ${\cal E}(\rho^{\otimes N})$ is {\it scalable} if it can be described as a function of the variables $\{{\cal E}(\rho^{\otimes i_1}),\dots,{\cal E}(\rho^{\otimes i_q}); N\}$ for $N>i_j$, while, preserving the tensor-product structure. If analyticity is assumed, recursive relations can be derived for the Maclaurin series of ${\cal E}(\rho^{\otimes N})$, which enable us to determine its possible functional forms (in terms of the mentioned variables). In particular, we find that if ${\cal E}(\rho^{\otimes 2^n})$ depends only on ${\cal E}(\rho)$, ${\cal E}(\rho^{\otimes 2})$, and $n$, then it is completely determined by Fibonacci polynomials, to leading order. We show that the one-shot distillable (OSD) entanglement is well described as a scalable measure for several families of states. For a particular two-qutrit state $\varrho$, we determine the OSD entanglement for $\varrho^{\otimes 96}$ from smaller tensorings, with an accuracy of $97 \%$ and no extra computational effort. Finally, we show that superactivation of non-additivity may occur in this context., Comment: Text enlarged and improved

In this work we investigate the probability of violation of local realism under random measurements in parallel with the strength of these violations as described by resistance to white noise admixture. We address multisetting Bell scenarios involving up to 7 qubits. As a result, in the first part of this manuscript we report statistical distributions of a quantity reciprocal to the critical visibility for various multipartite quantum states subjected to random measurements. The statistical relevance of different classes of multipartite tight Bell inequalities violated with random measurements is investigated. We also introduce the concept of typicality of quantum correlations for pure states as the probability to generate a nonlocal behaviour with both random state and measurement. Although this typicality is slightly above 5.3\% for the CHSH scenario, for a modest increase in the number of involved qubits it quickly surpasses 99.99\%., Comment: 5 pages, 5 figures

In this work, starting from commutation relations between phase-space operators (in "first quantization") we define averaged creation and annihilation operators and show that they satisfy a simple, deformed commutation relation. By extending this relation to the quantized electromagnetic field, we determine the new vacuum state which has a non-zero component in standard occupied states. In addition we are led to non-linear de Broglie relations for photons, which appreciably depart from linearity only in the very-high-energy regime. The nonlinear Compton scattering that follows from these assumptions is discussed. We suggest that this hypothesis may be a way to deal with the transparency of the electromagnetic background light (EBL) and show that it may lead to an attenuation in the cosmological-constant problem of several orders of magnitude., Comment: There is an important error in the second part of the manuscript, where, contrary to what is stated, Lorentz covariance is violated