UK energy strategies under uncertainty: synthesis report

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The Time-Energy Uncertainty Relation

The time energy uncertainty relation has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer (1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are concerned with different specific aspects of the subject. The purpose of this chapter is to show that different types of time energy uncertainty relation can indeed be deduced in specific contexts, but that there is no unique universal relation that could stand on equal footing with the position-momentum uncertainty relation. To this end, we will survey the various formulations of a time energy uncertainty relation, with a brief assessment of their validity, and along the way we will indicate some new developments that emerged since the 1990s.Comment: 33 pages, Latex. This expanded version (prepared for the 2nd edition of "Time in quantum mechanics") contains minor corrections, new examples and pointers to some additional relevant literatur

Bidding wind energy under uncertainty

The integration of wind energy into electricity markets implies that the wind energy must commit their production for a given time period. This requires the use of short term wind power prediction tools to prepare the bids for the spot market. The output of these tools have a limited accuracy, and, therefore, these predictions are uncertain. Optimal bids must take into account this uncertainty in order to get the maximum revenue from the sell of energy, minimizing losses due to imbalance costs. The consequence is that the optimal bids sent to the market do not coincide with the best predictions. Regulatory authorities must consider if this situation is good for the system operation, and encourage TSOs to have their own prediction tools and have results independent of bidding strategies.International Conference on Clean Electrical Power, ICCEP '07 (Capri, 21-23 May 2007). P. 754-759Publicad

Entropic Energy-Time Uncertainty Relation

Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to energy-time uncertainty because, in general, there is no Hermitian operator associated with time. Following previous approaches, we quantify time uncertainty by how well one can read off the time from a quantum clock. We then use entropy to quantify the information-theoretic distinguishability of the various time states of the clock. Our main result is an entropic energy-time uncertainty relation for general time-independent Hamiltonians, stated for both the discrete-time and continuous-time cases. Our uncertainty relation is strong, in the sense that it allows for a quantum memory to help reduce the uncertainty, and this formulation leads us to reinterpret it as a bound on the relative entropy of asymmetry. Due to the operational relevance of entropy, we anticipate that our uncertainty relation will have information-processing applications.Comment: 6 + 9 pages, 2 figure

Remarks on time-energy uncertainty relations

Using a recent construction of observables characterizing the time of occurence of an effect in quantum theory, we present a rigorous derivation of the standard time-energy uncertainty relation. In addition, we prove an uncertainty relation for time measurements only.Comment: 9 pages, to be pubblished in Rev. Math. Phys. issue in honor of H. Arak

Does oil price uncertainty affect energy use?

Theory predicts that the presence of fixed costs affects the relationship between energy use and energy price changes, as the firm's output and investment decisions respond differently to energy price increases and decreases. The asymmetry in response to energy price changes is exacerbated by uncertainty with respect to future energy prices, but to date the empirical literature does not explicitly take uncertainty into account. The contribution of this paper is twofold. First, we develop a new measure of energy price uncertainty. Second, we apply the measure to explain energy use in 8 OECD countries between 1978 and 1996, trying to identify whether indeed energy price uncertainty effects the asymmetry resulting from changes in energy use.