Ignorance based inference of optimality in thermodynamic processes

We derive ignorance based prior distribution to quantify incomplete information and show its use to estimate the optimal work characteristics of a heat engine.Comment: Latex, 10 pages, 3 figure

Geometry of escort distributions

Given an original distribution, its statistical and probabilistic attributs may be scanned by the associated escort distribution introduced by Beck and Schlogl and employed in the formulation of nonextensive statistical mechanics. Here, the geometric structure of the one-parameter family of the escort distributions is studied based on the Kullback-Leibler divergence and the relevant Fisher metric. It is shown that the Fisher metric is given in terms of the generalized bit-variance, which measures fluctuations of the crowding index of a multifractal. The Cramer-Rao inequality leads to the fundamental limit for precision of statistical estimate of the order of the escort distribution. It is also quantitatively discussed how inappropriate it is to use the original distribution instead of the escort distribution for calculating the expectation values of physical quantities in nonextensive statistical mechanics.Comment: 12 pages, no figure

(How) does productivity matter in the foundational economy?

Academics and policy makers have increasingly recognised the importance of mundane economic activities – variously termed foundational or everyday – by academics and policy makers. The foundational or everyday economy is now featuring in local industrial strategy and economic action plans, because the desirable high-tech sectors on the ‘frontier’ cannot diffuse prosperity within and between regions. This paper aims to distinguish between several different approaches to the foundational or everyday economy and argues that a constructive approach needs to break with the preoccupation about improving productivity. This argument is developed in three stages. First, we distinguish between a social approach and a more technical economic approach to delimiting this other mundane economy; the defining feature of the foundational in the social approach is contribution to wellbeing and in the technical economic approach it is low productivity. The second section presents and explores productivity evidence on output per worker hour across a range of foundational activities and by region. Drawing out the implications of observed diversity and heterogeneity, the third section develops an argument about how productivity has limited relevance as measure and target in foundational activitie

Neither Fear Nor Favour, Affection Or Ill Will: Modernisation of care proceedings and the use and value of independent social work expertise to senior judges

This is part two of an evaluation of the work of independent social work experts (ISWs) in care proceedings (stage I was published in April 2012). It takes forward findings from stage I exploring further the evidential base for views put to the Family Justice Review about the practice of courts. It examines the views, experiences and practices of a sample of senior judges in commissioning ISW assessments, placing these in the context of the timing, format and value of local authority assessments. Finally, judges? views about the implications of the modernisation programme for use of ISWs are explored - in the light of a need for earlier completion of cases, without loss of quality in assessments, and with regard to issues of fairness, justice and transparency in judicial decision making. In the report each section is followed by a summary of findings reflecting the key issue for policy and practice. The study is based on interviews with 23 senior judges (20 DFJs, 3 Circuit Judges) in 20/43 county courts in England and Wales. Interviews were held between February and April 2013. They include representation from all circuits, and courts with small and high volume case loads (less than 115, 251 - 900 applications in 12 months). They hear applications from just over half of authorities in England (59%) and just over one third (36%) in Wales

The contribution of experts in care proceedings : evaluation of independent social work reports on care proceedings

Several concerns surround the use of independent social work (ISW) assessments in care proceedings. Some result from the exclusion of this work from a review of legal aid for expert assessments in this field, a cap on ISW fees, and fears about a resulting reduction in the availability of ISWs. At the same time, submissions to the Family Justice Review (FJR) claimed that ISWs cause delay, simply duplicate existing local authority assessments, add nothing new and undermine confidence in social work assessments. It was also said that ISW reports result from parents utilising human rights claims to gain a second opinion of a local authority assessment ? and to which courts too readily accede. ... But while strong views have been expressed about the use of independent social work assessments, there is little hard evidence. This evaluation, commissioned following submissions to the FJR, begins to address that lack. It is based on 65 cases concerning 121 children and 82 reports for courts in England and Wales. The sample was drawn from the records of three independent agencies providing ISWs

Generalized symmetric nonextensive thermostatistics and q-modified structures

We formulate a convenient generalization of the q-expectation value, based on the analogy of the symmetric quantum groups and q-calculus, and show that the q->q^{-1} symmetric nonextensive entropy preserves all of the mathematical structure of thermodynamics just as in the case of non-symmetric Tsallis statistics. Basic properties and analogies with quantum groups are discussed.Comment: 9 pages, 1 figure. To appear in Mod. Phys. Lett.

Statistical Mechanics in the Extended Gaussian Ensemble

The extended gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. The new ensemble is a further extension of the Gaussian ensemble introduced by J. H. Hetherington [J. Low Temp. Phys. {\bf 66}, 145 (1987)]. The statistical mechanical formalism is derived both from the analysis of the system attached to a finite reservoir and from the Maximum Statistical Entropy Principle. The probability of each microstate depends on two parameters $\beta$ and $\gamma$ which allow to fix, independently, the mean energy of the system and the energy fluctuations respectively. We establish the Legendre transform structure for the generalized thermodynamic potential and propose a stability criterion. We also compare the EGE probability distribution with the $q$-exponential distribution. As an example, an application to a system with few independent spins is presented.Comment: Revtex 4, 8 pages, 8 figure

Informative priors and the analogy between quantum and classical heat engines

When incomplete information about the control parameters is quantified as a prior distribution, a subtle connection emerges between quantum heat engines and their classical analogs. We study the quantum model where the uncertain parameters are the intrinsic energy scales and compare with the classical models where the intermediate temperature is the uncertain parameter. The prior distribution quantifying the incomplete information has the form $\pi(x)\propto 1/x$ in both the quantum and the classical models. The expected efficiency calculated in near-equilibrium limit approaches the value of one third of Carnot efficiency.Comment: Revtex 6 pages, Submitted for Proceedings of Frontiers of Quantum and Mesoscopic Thermodynamics (FQMT-2011) Conferenc

Nonextensive Entropies derived from Form Invariance of Pseudoadditivity

The form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies. Nonextensive entropy is defined as the appropriate expectation value of nonextensive information content, similar to the definition of Shannon entropy. Information content in a nonextensive system is obtained uniquely from generalized axioms by replacing the usual additivity with pseudoadditivity. The satisfaction of the form invariance of the pseudoadditivity of nonextensive entropy and its information content is found to require the normalization of nonextensive entropies. The proposed principle requires the same normalization as that derived in [A.K. Rajagopal and S. Abe, Phys. Rev. Lett. {\bf 83}, 1711 (1999)], but is simpler and establishes a basis for the systematic definition of various entropies in nonextensive systems.Comment: 16 pages, accepted for publication in Physical Review