The foundations of statistical mechanics from entanglement: Individual states vs. averages

We consider an alternative approach to the foundations of statistical mechanics, in which subjective randomness, ensemble-averaging or time-averaging are not required. Instead, the universe (i.e. the system together with a sufficiently large environment) is in a quantum pure state subject to a global constraint, and thermalisation results from entanglement between system and environment. We formulate and prove a "General Canonical Principle", which states that the system will be thermalised for almost all pure states of the universe, and provide rigorous quantitative bounds using Levy's Lemma.Comment: 12 pages, v3 title changed, v2 minor change

The Vulnverability Cube: A Multi-Dimensional Framework for Assessing Relative Vulnerability

The diversity and abundance of information available for vulnerability assessments can present a challenge to decision-makers. Here we propose a framework to aggregate and present socioeconomic and environmental data in a visual vulnerability assessment that will help prioritize management options for communities vulnerable to environmental change. Socioeconomic and environmental data are aggregated into distinct categorical indices across three dimensions and arranged in a cube, so that individual communities can be plotted in a three-dimensional space to assess the type and relative magnitude of the communities’ vulnerabilities based on their position in the cube. We present an example assessment using a subset of the USEPA National Estuary Program (NEP) estuaries: coastal communities vulnerable to the effects of environmental change on ecosystem health and water quality. Using three categorical indices created from a pool of publicly available data (socioeconomic index, land use index, estuary condition index), the estuaries were ranked based on their normalized averaged scores and then plotted along the three axes to form a vulnerability cube. The position of each community within the three-dimensional space communicates both the types of vulnerability endemic to each estuary and allows for the clustering of estuaries with like-vulnerabilities to be classified into typologies. The typologies highlight specific vulnerability descriptions that may be helpful in creating specific management strategies. The data used to create the categorical indices are flexible depending on the goals of the decision makers, as different data should be chosen based on availability or importance to the system. Therefore, the analysis can be tailored to specific types of communities, allowing a data rich process to inform decision-making

Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular "reactive oxygen species" (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation. We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation). The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible. This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference

A topological application of the isoperimetric inequality

Many infinite dimensional topological spaces come with natural uniform structure, often associated to a metric. As an example one can take the Hilbert space H', the sphere S5 C H' or the Grassmann manifold Gk(Ho). We show in this paper that passing from the category of continuous maps to the category of uniformly continuous maps has a non-trivial effect on the homotopy theory. In particular we exhibit some natural fibrations which have continuous sections but have no uniformly continuous (in particular Lipschitz) sections. 1. The Levy measure. For a set A in a metric space X we denote by N(A ), e ? 0, its e-neighborhood. Consider a family {Xi, Ai}, i = 1, 2, ..., of metric spaces Xi with normalized (i.e. Ai(Xi) = 1) Borel measures Ai. We call such a family Levy if for any sequence of Borel sets Ai C Xi, i = 1, 2, . . ., such that lim infi ,0 Ai(Aj) > 0, and for every e > 0 we have limi<,. Mi(Nj(Ai)) = 1. 1.1. Principal Example. Let Xi be isometric to the Euclidean sphere Si C R '+ of radius ri. Take for ,ui the normalized i-dimensional volume element on S'. The family {Xi, Ai } is Levy iff rii-F12 -i,o 0 (see [6]). Proof. Let A C Si be an arbitrary Borel set and let B C Si be a ball (relative to the Riemannian metric in Si) such that /i(B) = ,ui(A). According to the isoperimetric inequality (see [12], [4]) one has Mi(NE(B)) < Ai(NE(A)), e > 0, and the general problem is reduced to the case when Ai are balls. A straight-forward calculation (see for instance, [6], [8]) yields now our assertio