Entropy on Spin Factors

Recently it has been demonstrated that the Shannon entropy or the von Neuman entropy are the only entropy functions that generate a local Bregman divergences as long as the state space has rank 3 or higher. In this paper we will study the properties of Bregman divergences for convex bodies of rank 2. The two most important convex bodies of rank 2 can be identified with the bit and the qubit. We demonstrate that if a convex body of rank 2 has a Bregman divergence that satisfies sufficiency then the convex body is spectral and if the Bregman divergence is monotone then the convex body has the shape of a ball. A ball can be represented as the state space of a spin factor, which is the most simple type of Jordan algebra. We also study the existence of recovery maps for Bregman divergences on spin factors. In general the convex bodies of rank 2 appear as faces of state spaces of higher rank. Therefore our results give strong restrictions on which convex bodies could be the state space of a physical system with a well-behaved entropy function.Comment: 30 pages, 6 figure

On Convergence Properties of Shannon Entropy

Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential entropies. A general result for the desired differential entropy convergence is provided, taking into account both compactly and uncompactly supported densities. Convergence of differential entropy is also characterized in terms of the Kullback-Liebler discriminant for densities with fairly general supports, and it is shown that convergence in variation of probability measures guarantees such convergence under an appropriate boundedness condition on the densities involved. Results for the discrete setting are also provided, allowing for infinitely supported probability measures, by taking advantage of the equivalence between weak convergence and convergence in variation in this setting.Comment: Submitted to IEEE Transactions on Information Theor

On the origin of ambiguity in efficient communication

This article studies the emergence of ambiguity in communication through the concept of logical irreversibility and within the framework of Shannon's information theory. This leads us to a precise and general expression of the intuition behind Zipf's vocabulary balance in terms of a symmetry equation between the complexities of the coding and the decoding processes that imposes an unavoidable amount of logical uncertainty in natural communication. Accordingly, the emergence of irreversible computations is required if the complexities of the coding and the decoding processes are balanced in a symmetric scenario, which means that the emergence of ambiguous codes is a necessary condition for natural communication to succeed.Comment: 28 pages, 2 figure

Deliberating stratospheric aerosols for climate geoengineering and the SPICE project

Increasing concerns about the narrowing window for averting dangerous climate change have prompted calls for research into geoengineering, alongside dialogue with the public regarding this as a possible response. We report results of the first public engagement study to explore the ethics and acceptability of stratospheric aerosol technology and a proposed field trial (the Stratospheric Particle Injection for Climate Engineering (SPICE) ‘pipe and balloon’ test bed) of components for an aerosol deployment mechanism. Although almost all of our participants were willing to allow the field trial to proceed, very few were comfortable with using stratospheric aerosols. This Perspective also discusses how these findings were used in a responsible innovation process for the SPICE project initiated by the UK’s research councils

Pylons in the back yard: local planning and perceived risks to health

Health fears arising from the presence of high-voltage power lines in residential areas have received recent attention in spatial planning. A study of stances taken by planning authorities in England and Wales shows their willingness to give expression to the concerns of local communities through precautionary measures, and the difficulties encountered in the face of official statements and industry opposition. These attempts to embody local feeling in patterns of development are illustrative of the increasing prevalence of a sense of risk in contemporary society. The spatial patterns of risk are also revealed, which owe much to the presence and distribution of industrial infrastructure in the landscape and to the associated contested use of land.</p

Ethics and ‘fracking’: A review of (the limited) moral thought on shale gas development

Whilst claims about the ethicality of shale gas development via hydraulic fracturing (‘fracking’) are commonplace in everyday discourse, little scholarly attention has been afforded explicitly to this aspect of unconventional fossil fuel extraction. The limited research that speaks to ethical considerations largely describes ethical concerns associated with development – extremely few claims in research literature make an ethical case for development. The most common ethical concerns cited in research stem from issues of distributive justice, with procedural justice, the precautionary principle, exposure to involuntary risks, rights-based arguments, and changes in community character and way of life as next most common. Additional research hints implicitly at ethical dilemmas associated with shale gas development, but does not openly identify these issues as having moral implications. Many ethical considerations relate closely to concerns about water quality and the volume/supply of water available for other purposes. The limited scholarship in this area reveals the import of understanding the ways in which ethics permeate thoughts about shale gas development for designing policy that responds to constituent needs and concerns. Even more limited than research on ethical claims in association with shale gas development is well-reasoned scholarship that analyses the extent to which ethical claims about development are well justified and philosophically justifiable. A comprehensive and systematic analysis of the range of ethical claims potentially relevant to shale gas development and their usefulness for informing policy on this topic would contribute greatly to informed decision-making on this controversial issue – something that science alone cannot achieve