Ideal Gas in a strong Gravitational field: Area dependence of Entropy

We study the thermodynamic parameters like entropy, energy etc. of a box of gas made up of indistinguishable particles when the box is kept in various static background spacetimes having a horizon. We compute the thermodynamic variables using both statistical mechanics as well as by solving the hydrodynamical equations for the system. When the box is far away from the horizon, the entropy of the gas depends on the volume of the box except for small corrections due to background geometry. As the box is moved closer to the horizon with one (leading) edge of the box at about Planck length (L_p) away from the horizon, the entropy shows an area dependence rather than a volume dependence. More precisely, it depends on a small volume A*L_p/2 of the box, upto an order O(L_p/K)^2 where A is the transverse area of the box and K is the (proper) longitudinal size of the box related to the distance between leading and trailing edge in the vertical direction (i.e in the direction of the gravitational field). Thus the contribution to the entropy comes from only a fraction O(L_p/K) of the matter degrees of freedom and the rest are suppressed when the box approaches the horizon. Near the horizon all the thermodynamical quantities behave as though the box of gas has a volume A*L_p/2 and is kept in a Minkowski spacetime. These effects are: (i) purely kinematic in their origin and are independent of the spacetime curvature (in the sense that Rindler approximation of the metric near the horizon can reproduce the results) and (ii) observer dependent. When the equilibrium temperature of the gas is taken to be equal to the the horizon temperature, we get the familiar A/L_p^2 dependence in the expression for entropy. All these results hold in a D+1 dimensional spherically symmetric spacetime.Comment: 19 pages, added some discussion, matches published versio

Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity

We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients \eta and \zeta of the membrane fluid. We show that the membrane pressure is intimately connected with the Noether charge entropy S_Wald of the horizon when we consider a specific m-th order Lanczos-Lovelock model, through the relation pA/T=(D-2m)/(D-2)S_Wald, where T is the temperature and A is the area of the horizon. Similarly, the viscosity coefficients are expressible in terms of entropy and quasi-local energy associated with the horizons. The bulk and shear viscosity coefficients are found to obey the relation \zeta=-2(D-3)/(D-2)\eta.Comment: v1: 13 pages, no figure. (v2): refs added, typos corrected, new subsection added on the ratio \eta/s. (v3): some clarification added, typos corrected, to appear in JHE

Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions

The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general co-variance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension $D = 2m$ and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in $D = 2m$. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In particular, we demonstrate that, in two dimensions, $R \sqrt{-g} = \partial_j R^j$ for a doublet of functions $R^j = (R^0,R^1)$ which depends only on the metric and its first derivatives. We explicitly construct families of such R^j -s in two dimensions. We also address related questions regarding the Gauss-Bonnet Lagrangian in $D = 4$. Finally, we demonstrate the relation between the Chern-Simons form and the mth order Lanczos-Lovelock Lagrangian.Comment: 15 pages, no figure

Study on Morbidity and Mortality Rates in Buffaloes in Pune Division of Maharashtra State in India

The present study was carried out to analyse morbidity and mortality rate in buffaloes and its associated factors in Pune division of Maharashtra state in India. Stratified two stages random sampling design was adopted & the data of total 564 buffaloes were collected through pre-tested modified schedule from 157 buffalo owners. The data were analysed statistically by SAS 9.3 software for evaluation of Chi-square and Logistic regression analysis. Overall morbidity (28.01%) and mortality (7.98%) rates were recorded in study area. Digestive diseases and respiratory diseases are major cause of the higher morbidity and mortality in buffaloes, respectively. Statistically, there wasn't significant association of overall disease incidence with age or sex. However, the Chi-square analysis of overall mortality rate showed significance (p<0.01) difference among age and sex. Logistic regression analysis also suggested the same results. Mortality rates were recorded higher in calves and male buffaloes as compared to their respective counterparts. It is suggested that digestive and respiratory problems may be reduced by improving feeding and management practices. This study provides the important tool for determining the health status of buffaloes and has special importance in planning of prevention and control strategies designed to reduce the incidences of diseases in livestock and therefore economic status of farmers

SmartTennisTV: Automatic indexing of tennis videos

In this paper, we demonstrate a score based indexing approach for tennis videos. Given a broadcast tennis video (BTV), we index all the video segments with their scores to create a navigable and searchable match. Our approach temporally segments the rallies in the video and then recognizes the scores from each of the segments, before refining the scores using the knowledge of the tennis scoring system. We finally build an interface to effortlessly retrieve and view the relevant video segments by also automatically tagging the segmented rallies with human accessible tags such as 'fault' and 'deuce'. The efficiency of our approach is demonstrated on BTV's from two major tennis tournaments.Comment: 10 pages, 4 figures, NCVPRIPG 2017 Accepted Paper (Best Paper Award Winner

Entropy bounds in terms of the w parameter

In a pair of recent articles [PRL 105 (2010) 041302 - arXiv:1005.1132; JHEP 1103 (2011) 056 - arXiv:1012.2867] two of the current authors have developed an entropy bound for equilibrium uncollapsed matter using only classical general relativity, basic thermodynamics, and the Unruh effect. An odd feature of that bound, S <= A/2, was that the proportionality constant, 1/2, was weaker than that expected from black hole thermodynamics, 1/4. In the current article we strengthen the previous results by obtaining a bound involving the (suitably averaged) w parameter. Simple causality arguments restrict this averaged parameter to be <= 1. When equality holds, the entropy bound saturates at the value expected based on black hole thermodynamics. We also add some clarifying comments regarding the (net) positivity of the chemical potential. Overall, we find that even in the absence of any black hole region, we can nevertheless get arbitrarily close to the Bekenstein entropy.Comment: V1: 14 pages. V2: One reference added. V3: This version accepted for publication in JHE

Productivity attributes of six desi cow breeds in Karnataka

Desi cows are playing crucial role in the national economy for their draught power, milk, dung, fuel and urine. It is a source of subsidiary income for many families in India especially the resource poor. The present study was carried out in six districts of Karnataka with higher population of each of the six desi breeds. Forty farmers served as respondents for each breed, making the total sample size of 240 farm households. Deoni productivity was the best with 3.85 L/anim./day followed by 3.07 in case of Krishna Valley. Daily net return per animal was ₹ 18.20 in Deoni and ₹ 15.51 in Krishna Valley, while it was lowest in Malnad Gidda. Without considering cost of fodder, net return (₹/anim./day) was the highest for Hallikar followed by Deoni and Krishna Valley. Draught power, dual purpose utility, quality and taste of milk, adaptability to harsh tropical climate, religious sentiments and social esteem were the important attributes of desi cows. Natural service, open grazing, feeding concentrates, green fodder and hay, closed housing system, vaccination, utility of dung and urine in the farm, full hand milking method were the management strategies adopted. Shrinking holding size, non-availability of grazing land, longer inter-calving period, and poor milk production were the important constraints perceived by farmers. Non-availability of superior quality breeding bulls and high price of cattle feed were perceived as causes for decreasing indigenous cattle population

The enrichment of an alkaliphilic biofilm consortia capable of the anaerobic degradation of isosaccharinic acid from cellulosic materials incubated within an anthropogenic, hyperalkaline environment.

Anthropogenic hyper-alkaline sites provide an environment that is analogous to proposed cementitious geological disposal facilities (GDF) for radioactive waste. Under anoxic, alkaline conditions cellulosic wastes will hydrolyse to a range of cellulose degradation products (CDP) dominated by isosaccharinic acids (ISA). In order to investigate the potential for microbial activity in a cementitious GDF, cellulose samples were incubated in the alkaline (∼pH 12), anaerobic zone of a lime kiln waste site. Following retrieval, these samples had undergone partial alkaline hydrolysis and were colonised by a Clostridia dominated biofilm community, where hydrogenotrophic, alkaliphilic methanogens were also present. When these samples were used to establish an alkaline CDP fed microcosm, the community shifted away from Clostridia, methanogens became undetectable and a flocculate community dominated by Alishewanella sp. established. These flocs were composed of bacteria embedded in polysaccharides and protein stabilised by extracellular DNA. This community was able to degrade all forms of ISA with >60% of the carbon flow being channelled into extracellular polymeric substance (EPS) production. This study demonstrated that alkaliphilic microbial communities can degrade the CDP associated with some radioactive waste disposal concepts at pH 11. These communities divert significant amounts of degradable carbon to EPS formation, suggesting that EPS has a central role in the protection of these communities from hyper-alkaline conditions

Black hole thermodynamical entropy

As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy $S_{BG}$ of a $(3+1)$ black hole is proportional to its area $L^2$ ($L$ being a characteristic linear length), and not to its volume $L^3$. Similarly it exists the \emph{area law}, so named because, for a wide class of strongly quantum-entangled $d$-dimensional systems, $S_{BG}$ is proportional to $\ln L$ if $d=1$, and to $L^{d-1}$ if $d>1$, instead of being proportional to $L^d$ ($d \ge 1$). These results violate the extensivity of the thermodynamical entropy of a $d$-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is \emph{not} to be identified with the BG {\it additive} entropy but with appropriately generalized {\it nonadditive} entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle.Comment: 7 pages, 2 figures. Accepted for publication in EPJ