General properties of entropy
It is rather self-contradictory that, though entropy is one among the foremost vital quantities in physics, its main properties area unit seldom listed within the usual textbooks on natural philosophy. during this paper we tend to try and fill this gap by discussing these properties, as, for example, invariance, additivity, concavity, subadditivity, sturdy subadditivity, continuity, etc., in detail, with relation to their implications in natural philosophy. additionally, we tend to think about connected ideas like relative entropy, skew entropy, high-vo entropy, etc. Taking under consideration that natural philosophy deals with massive, basically infinite systems, we tend to finally can get a glimpse of systems with infinitely several degrees of freedom. [1]
Entropy Inequalities
Some inequalities and relations among entropies of reduced quantum mechanical density matrices are mentioned and tried. whereas these don’t seem to be as sturdy as those accessible for classical systems they’re yet powerful enough to ascertain the existence of the limiting mean entropy for translationally invariant states of quantum continuous systems. [2]
Entropy and diversity
Entropies like the Shannon–Wiener and Gini–Simpson indices aren’t themselves diversities. Conversion of those to effective variety of species is that the key to a unified and intuitive interpretation of diversity. Effective numbers of species derived from standard diversity indices share a standard set of intuitive mathematical properties and behave in concert would expect of a diversity, whereas raw indices don’t. Contrary to Keylock, the shortage of concavity of effective numbers of species is impertinent as long as they’re used as transformations of cotyloidal alpha, beta, and gamma entropies. the sensible importance of this transformation is incontestable by applying it to a preferred community similarity live supported raw diversity indices or entropies. the quality similarity live supported untransformed indices is shown to administer dishonest results, however reworking the indices or entropies to effective numbers of species produces a stable, simply understood, sensitive general similarity live. [3]
Ranking Regions, Edges and Classifying Tasks in Functional Brain Graphs by Sub-Graph Entropy
This paper considers analysis of human brain networks or graphs made from time-series collected from purposeful resonance imaging (fMRI). within the network of time-series, the nodes describe the regions and also the edge weights correspond to absolutely the values of correlation coefficients of the time-series of the 2 nodes related to the sides. The paper introduces a completely unique information-theoretic metric, referred as sub-graph entropy, to live uncertainty related to a sub-graph. Nodes and edges represent 2 special cases of sub-graph structures. Node and edge entropies ar utilized in this paper to rank regions and edges in an exceedingly purposeful brain network. The paper analyzes task-fMRI information collected from 475 subjects within the Human Connectome Project (HCP) study for gambling and feeling tasks. The planned approach is employed to rank regions and edges related to these tasks. [4]
Temperature Induced Conformational Entropy of α-Amylase with and without Additive
Aims: 1) To formulate models supported outlined principle for the appliance of Fitter’s model associate degreed 2) ultimately show that there are modifications within the radius of an accelerator in resolution and consequently S change with temperature before and through chemical process activity.
Study Design: Theoretical and experimental.
Place and length of Study: Department of Chemistry and organic chemistry, analysis Division, Ude International ideas LTD (862217), B. B. Agbor, Delta State, Nigeria; Owa Alizomor lyceum, Owa Alizomor, Ika North East, Delta State, Nigeria. The analysis was conducted between June and December, 2016.
Methodology: Bernfeld methodology of accelerator assay was used. Assays were allotted on diluted crude human secretion alpha enzyme (HSaA). information from assay were premeditated in 2 ways that viz: rate (v) vs physical science temperature (T) and 1/v vs T. quotient constants were determined from slope and intercept of the simple regression. These were wont to verify desired parameters. [5]
Reference
[1] Wehrl, A., 1978. General properties of entropy. Reviews of Modern Physics, 50(2), (Web Link)
[2] Araki, H. and Lieb, E.H., 2002. Entropy inequalities. In Inequalities (pp. 47-57). Springer, Berlin, Heidelberg. (Web Link)
[3] Jost, L., 2006. Entropy and diversity. Oikos, 113(2), (Web Link)
[4] Ranking Regions, Edges and Classifying Tasks in Functional Brain Graphs by Sub-Graph Entropy
Bhaskar Sen, Shu-Hsien Chu & Keshab K. Parhi
Scientific Reports volume 9, Article number: 7628 (2019) (Web Link)
[5] I. Udema, I. (2017) “Temperature Induced Conformational Entropy of α-Amylase with and without Additive”, International Journal of Biochemistry Research & Review, 16(1), (Web Link)