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The work content of non-equilibrium systems in relation to a heat bath is often analysed in terms of expectation values of an underlying random work variable. However, when optimizing the expectation value of the extracted work, the resulting extraction process is subject to intrinsic fluctuations, uniquely determined by the Hamiltonian and the initial distribution of the system. These fluctuations can be of the same order as the expected work content per se , in which case the extracted energy is unpredictable, thus intuitively more heat-like than work-like. This raises the question of the ‘truly’ work-like energy that can be extracted. Here we consider an alternative that corresponds to an essentially fluctuation-free extraction. We show that this quantity can be expressed in terms of a one-shot relative entropy measure introduced in information theory. This suggests that the relations between information theory and statistical mechanics, as illustrated by concepts like Maxwell’s demon, Szilard engines and Landauer’s principle, extends to the single-shot regime. Thermodynamics and information theory are closely related but the fundamental limitations of this relation are difficult to determine. Combining concepts from one-shot information theory, probability theory and statistical mechanics, the author quantifies extractable work in a non-equilibrium system.

Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce “conditional” fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

Cool computations Landauer's erasure principle, a widely accepted part of classical information theory first proposed by Rolf Landauer in 1961, asserts that it is necessary to perform work in order to erase data. This occurs when carrying out irreversible operations, thus releasing heat to the environment. For example, in electronics, heat generation is a major obstacle to circuitry miniaturization. Del Rio et al . show that the situation is completely different in the presence of quantum information about the system, and the implications of Landauer's principle are invalid. The more that is known about a system, the less it costs to erase it. An observer who is strongly correlated with a system may even gain work while erasing it, therefore cooling the environment. The quantum systems needed to experimentally demonstrate these results are, in principle, accessible with current technology. The heat generated by computations is not only an obstacle to circuit miniaturization but also a fundamental aspect of the relationship between information theory and thermodynamics. In principle, reversible operations may be performed at no energy cost; given that irreversible computations can always be decomposed into reversible operations followed by the erasure of data 1 , 2 , the problem of calculating their energy cost is reduced to the study of erasure. Landauer’s principle states that the erasure of data stored in a system has an inherent work cost and therefore dissipates heat 3 , 4 , 5 , 6 , 7 , 8 . However, this consideration assumes that the information about the system to be erased is classical, and does not extend to the general case where an observer may have quantum information about the system to be erased, for instance by means of a quantum memory entangled with the system. Here we show that the standard formulation and implications of Landauer’s principle are no longer valid in the presence of quantum information. Our main result is that the work cost of erasure is determined by the entropy of the system, conditioned on the quantum information an observer has about it. In other words, the more an observer knows about the system, the less it costs to erase it. This result gives a direct thermodynamic significance to conditional entropies, originally introduced in information theory. Furthermore, it provides new bounds on the heat generation of computations: because conditional entropies can become negative in the quantum case, an observer who is strongly correlated with a system may gain work while erasing it, thereby cooling the environment.

Electronic commerce has recently shown enormous potential to take over a significant share of the sales market. There is a need to provide services that can reach individual computer users with different information profiles and levels of expertise. In this article the concept of Web assistants, human assistants working in an electronic Web shop, is presented. This human-computer collaboration provides intelligent and adaptive services via an integrated communication media. A prototype of a Web assistant system has been implemented. While browsing through the system the user can call for human assistance should the need arise. Presents the results of a usability study performed on the prototype system. Recent commercial moves in the direction discussed in this article increase the importance of the usability study. The results are encouraging, especially when it comes to the attitude aspects of usability. The subjects were extremely enthusiastic about the concept of Web assistants and its implications. The human Web assistant who participated in the field trial highlighted the importance of user modelling. Although the system is mainly in the context of electronic commerce, it can be used in many other contexts. These include home automation, digital libraries, and technical support, to name a few.

Quantum networks play a major role in long-distance communication, quantum cryptography, clock synchronization, and distributed quantum computing. Generally, these protocols involve many independent sources sharing entanglement among distant parties that, upon measuring their systems, generate correlations across the network. The question of which correlations a given quantum network can give rise to, remains almost uncharted. Here we show that constraints on the observable covariances, previously derived for the classical case, also hold for quantum networks. The network topology yields tests that can be cast as semidefinite programs, thus allowing for the efficient characterization of the correlations in a wide class of quantum networks, as well as systematic derivations of device-independent and experimentally testable witnesses. We obtain such semidefinite tests for fixed measurement settings, as well as parties that independently choose among collections of measurement settings. The applicability of the method is demonstrated for various networks, and compared with previous approaches.

Many search-based quantum algorithms that achieve a theoretical speedup are not practically relevant since they require extraordinarily long coherence times, or lack the parallelizability of their classical counterparts.This raises the question of how to divide computational tasks into a collection of parallelizable sub-problems, each of which can be solved by a quantum computer with limited coherence time. Here, we approach this question via hybrid algorithms for the k-SAT problem. Our analysis is based on Sch\"oning's algorithm, which solves instances of k-SAT by performing random walks in the space of potential assignments. The search space of the walk allows for \"natural\" partitions, where we subject only one part of the partition to a Grover search, while the rest is sampled classically, thus resulting in a hybrid scheme. In this setting, we argue that there exists a simple trade-off relation between the total runtime and the coherence-time, which no such partition based hybrid-scheme can surpass. For several concrete choices of partitions, we explicitly determine the specific runtime coherence-time relations, and show saturation of the ideal trade-off. Finally, we present numerical simulations which suggest additional flexibility in implementing hybrid algorithms with optimal trade-off.

We show that the norm squared amplitudes with respect to a local orthonormal basis (the classical restriction) of finite quantum systems on one-dimensional lattices can be exponentially well approximated by Gibbs states of local Hamiltonians (i.e., are quasi-locally Gibbsian) if the classical conditional mutual information (CMI) of any connected tripartition of the lattice is rapidly decaying in the width of the middle region. For injective matrix product states, we moreover show that the classical CMI decays exponentially, whenever the collection of matrix product operators satisfies a 'purity condition'; a notion previously established in the theory of random matrix products. We furthermore show that violations of the purity condition enables a generalized notion of error correction on the virtual space, thus indicating the non-generic nature of such violations. We make this intuition more concrete by constructing a probabilistic model where purity is a typical property. The proof of our main result makes extensive use of the theory of random matrix products, and may find applications elsewhere.

The aim of this study was to evaluate the effects of habitat fragment size and isolation on the dynamics of hazel grouse (Bonasa bonasia L.) occurrence. Habitat fragments surrounded by nonhabitat coniferous forest, in an intensively managed forested landscape, were censused during seven seasons.

Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs with the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy, and the control system that implements the dynamic, we here obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir, but the full description of its evolution, including coherences. This approach moreover opens up for generalizations of the concept of fluctuation relations. Here we introduce `conditional' fluctuation relations that are applicable to non-equilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.