Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains

Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics

Complete Break Up of Ortho Positronium (Ps)- Hydrogenic ion System

The dynamics of the complete breakup process in an Ortho Ps - He+ system including electron loss to the continuum (ELC) is studied where both the projectile and the target get ionized. The process is essentially a four body problem and the present model takes account of the two centre effect on the electron ejected from the Ps atom which is crucial for a proper description of the ELC phenomena. The calculations are performed in the framework of Coulomb Distorted Eikonal Approximation. The exchange effect between the target and the projectile electron is taken into account in a consistent manner. The proper asymptotic 3-body boundary condition for this ionization process is also satisfied in the present model. A distinct broad ELC peak is noted in the fully differential cross sections (5DCS) for the Ps electron corroborating qualitatively the experiment for the Ps - He system. Both the dynamics of the ELC from the Ps and the ejected electron from the target He+ in the FDCS are studied using coplanar geometry. Interesting features are noted in the FDCS for both the electrons belonging to the target and the projectile.Comment: 14 pages,7 figure

Relic neutrino masses and the highest energy cosmic rays

We consider the possibility that a large fraction of the ultrahigh energy cosmic rays are decay products of Z bosons which were produced in the scattering of ultrahigh energy cosmic neutrinos on cosmological relic neutrinos. We compare the observed ultrahigh energy cosmic ray spectrum with the one predicted in the above Z-burst scenario and determine the required mass of the heaviest relic neutrino as well as the necessary ultrahigh energy cosmic neutrino flux via a maximum likelihood analysis. We show that the value of the neutrino mass obtained in this way is fairly robust against variations in presently unknown quantities, like the amount of neutrino clustering, the universal radio background, and the extragalactic magnetic field, within their anticipated uncertainties. Much stronger systematics arises from different possible assumptions about the diffuse background of ordinary cosmic rays from unresolved astrophysical sources. In the most plausible case that these ordinary cosmic rays are protons of extragalactic origin, one is lead to a required neutrino mass in the range 0.08 eV - 1.3 eV at the 68 % confidence level. This range narrows down considerably if a particular universal radio background is assumed, e.g. to 0.08 eV - 0.40 eV for a large one. The required flux of ultrahigh energy cosmic neutrinos near the resonant energy should be detected in the near future by AMANDA, RICE, and the Pierre Auger Observatory, otherwise the Z-burst scenario will be ruled out.Comment: 19 pages, 22 figures, REVTeX

Diabetes Prevalence and Its Relationship With Education, Wealth, and BMI in 29 Low- and Middle-Income Countries.

Diabetes is a rapidly growing health problem in low- and middle-income countries (LMICs), but empirical data on its prevalence and relationship to socioeconomic status are scarce. We estimated diabetes prevalence and the subset with undiagnosed diabetes in 29 LMICs and evaluated the relationship of education, household wealth, and BMI with diabetes risk. We pooled individual-level data from 29 nationally representative surveys conducted between 2008 and 2016, totaling 588,574 participants aged ≥25 years. Diabetes prevalence and the subset with undiagnosed diabetes was calculated overall and by country, World Bank income group (WBIG), and geographic region. Multivariable Poisson regression models were used to estimate relative risk (RR). Overall, prevalence of diabetes in 29 LMICs was 7.5% (95% CI 7.1-8.0) and of undiagnosed diabetes 4.9% (4.6-5.3). Diabetes prevalence increased with increasing WBIG: countries with low-income economies (LICs) 6.7% (5.5-8.1), lower-middle-income economies (LMIs) 7.1% (6.6-7.6), and upper-middle-income economies (UMIs) 8.2% (7.5-9.0). Compared with no formal education, greater educational attainment was associated with an increased risk of diabetes across WBIGs, after adjusting for BMI (LICs RR 1.47 [95% CI 1.22-1.78], LMIs 1.14 [1.06-1.23], and UMIs 1.28 [1.02-1.61]). Among 29 LMICs, diabetes prevalence was substantial and increased with increasing WBIG. In contrast to the association seen in high-income countries, diabetes risk was highest among those with greater educational attainment, independent of BMI. LMICs included in this analysis may be at an advanced stage in the nutrition transition but with no reversal in the socioeconomic gradient of diabetes risk

Body-mass index and diabetes risk in 57 low-income and middle-income countries: a cross-sectional study of nationally representative, individual-level data in 685 616 adults.

The prevalence of overweight, obesity, and diabetes is rising rapidly in low-income and middle-income countries (LMICs), but there are scant empirical data on the association between body-mass index (BMI) and diabetes in these settings. In this cross-sectional study, we pooled individual-level data from nationally representative surveys across 57 LMICs. We identified all countries in which a WHO Stepwise Approach to Surveillance (STEPS) survey had been done during a year in which the country fell into an eligible World Bank income group category. For LMICs that did not have a STEPS survey, did not have valid contact information, or declined our request for data, we did a systematic search for survey datasets. Eligible surveys were done during or after 2008; had individual-level data; were done in a low-income, lower-middle-income, or upper-middle-income country; were nationally representative; had a response rate of 50% or higher; contained a diabetes biomarker (either a blood glucose measurement or glycated haemoglobin [HbA <sub>1c</sub> ]); and contained data on height and weight. Diabetes was defined biologically as a fasting plasma glucose concentration of 7·0 mmol/L (126·0 mg/dL) or higher; a random plasma glucose concentration of 11·1 mmol/L (200·0 mg/dL) or higher; or a HbA <sub>1c</sub> of 6·5% (48·0 mmol/mol) or higher, or by self-reported use of diabetes medication. We included individuals aged 25 years or older with complete data on diabetes status, BMI (defined as normal [18·5-22·9 kg/m <sup>2</sup> ], upper-normal [23·0-24·9 kg/m <sup>2</sup> ], overweight [25·0-29·9 kg/m <sup>2</sup> ], or obese [≥30·0 kg/m <sup>2</sup> ]), sex, and age. Countries were categorised into six geographical regions: Latin America and the Caribbean, Europe and central Asia, east, south, and southeast Asia, sub-Saharan Africa, Middle East and north Africa, and Oceania. We estimated the association between BMI and diabetes risk by multivariable Poisson regression and receiver operating curve analyses, stratified by sex and geographical region. Our pooled dataset from 58 nationally representative surveys in 57 LMICs included 685 616 individuals. The overall prevalence of overweight was 27·2% (95% CI 26·6-27·8), of obesity was 21·0% (19·6-22·5), and of diabetes was 9·3% (8·4-10·2). In the pooled analysis, a higher risk of diabetes was observed at a BMI of 23 kg/m <sup>2</sup> or higher, with a 43% greater risk of diabetes for men and a 41% greater risk for women compared with a BMI of 18·5-22·9 kg/m <sup>2</sup> . Diabetes risk also increased steeply in individuals aged 35-44 years and in men aged 25-34 years in sub-Saharan Africa. In the stratified analyses, there was considerable regional variability in this association. Optimal BMI thresholds for diabetes screening ranged from 23·8 kg/m <sup>2</sup> among men in east, south, and southeast Asia to 28·3 kg/m <sup>2</sup> among women in the Middle East and north Africa and in Latin America and the Caribbean. The association between BMI and diabetes risk in LMICs is subject to substantial regional variability. Diabetes risk is greater at lower BMI thresholds and at younger ages than reflected in currently used BMI cutoffs for assessing diabetes risk. These findings offer an important insight to inform context-specific diabetes screening guidelines. Harvard T H Chan School of Public Health McLennan Fund: Dean's Challenge Grant Program