Boltzmann–shannon Entropy: Generalization and Application

Chakrabarti, C. G.; Chakrabarty, Indranil

doi:10.1142/s0217984906011529

Cited by 10 publications

(9 citation statements)

References 6 publications

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“…Thermodynamic probability

in formula (3) is not an ordinary probability, but an integer. However, it is possible to modify Boltzmann entropy to enable the introduction of the notion of probability distribution in Boltzmann statistics [ 8 ]. If an isolated system, consisting of

molecules belonging to n energy states is examined, then – assuming a fixed number of molecules and fixed values of the total energy – the total number of microscopic states of the system is given by the formula:

Substituting (4) to (3), Boltzmann entropy is obtained in the following form:

where

and for a large

means the probability that the molecule is in the i -th energy state.…”

Section: A Brief History Of the Emergence And Development Of The Ementioning

confidence: 99%

The Role of Entropy in the Development of Economics

Jakimowicz

2020

Entropy

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The aim of this paper is to examine the role of thermodynamics, and in particular, entropy, for the development of economics within the last 150 years. The use of entropy has not only led to a significant increase in economic knowledge, but also to the emergence of such scientific disciplines as econophysics, complexity economics and quantum economics. Nowadays, an interesting phenomenon can be observed; namely, that rapid progress in economics is being made outside the mainstream. The first significant achievement was the emergence of entropy economics in the early 1970s, which introduced the second law of thermodynamics to considerations regarding production processes. In this way, not only was ecological economics born but also an entropy-based econometric approach developed. This paper shows that non-extensive cross-entropy econometrics is a valuable complement to traditional econometrics as it explains phenomena based on power-law probability distribution and enables econometric model estimation for non-ergodic ill-behaved (troublesome) inverse problems. Furthermore, the entropy economics has accelerated the emergence of modern econophysics and complexity economics. These new directions of research have led to many interesting discoveries that usually contradict the claims of conventional economics. Econophysics has questioned the efficient market hypothesis, while complexity economics has shown that markets and economies function best near the edge of chaos. Quantum economics has already appeared on the horizon, which recognizes money as a fundamental measurement device in the economy. The development of these sciences may indicate the need to reformulate all mainstream economics from its foundations.

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“…Thermodynamic probability

Substituting (4) to (3), Boltzmann entropy is obtained in the following form:

where

and for a large

means the probability that the molecule is in the i -th energy state.…”

Section: A Brief History Of the Emergence And Development Of The Ementioning

confidence: 99%

The Role of Entropy in the Development of Economics

Jakimowicz

2020

Entropy

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“…26, 27 There is a known relationship between Shannon entropy and thermodynamic entropy in statistical mechanics, such that entropy can be used as a measure of the molecular disorder of a system. 28 Applications of entropy in communication theory provide a way to quantify the amount of information associated with a received message. 11 The amount of information gained by the receiver depends on the probability that a message (or event) will occur.…”

Section: Discussionmentioning

confidence: 99%

Using Weighted Entropy to Rank Chemicals in Quantitative High-Throughput Screening Experiments

Shockley

2014

SLAS Discovery

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Quantitative high throughput screening (qHTS) experiments can simultaneously produce concentration-response profiles for thousands of chemicals. In a typical qHTS study, a large chemical library is subjected to a primary screen in order to identify candidate hits for secondary screening, validation studies or prediction modeling. Different algorithms, usually based on the Hill equation logistic model, have been used to classify compounds as active or inactive (or inconclusive). However, observed concentration-response activity relationships may not adequately fit a sigmoidal curve. Furthermore, it is unclear how to prioritize chemicals for follow-up studies given the large uncertainties that often accompany parameter estimates from nonlinear models. Weighted Shannon entropy can address these concerns by ranking compounds according to profile-specific statistics derived from estimates of the probability mass distribution of response at the tested concentration levels. This strategy can be used to rank all tested chemicals in the absence of a pre-specified model structure or the approach can complement existing activity call algorithms by ranking the returned candidate hits. The weighted entropy approach was evaluated here using data simulated from the Hill equation model. The procedure was then applied to a chemical genomics profiling data set interrogating compounds for androgen receptor agonist activity.

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“…To visualize of the system sustainability transformation, it is advisable to use the negentropy index calculated using the Shannon formula [Chen, Li, 2011;Chakrabarti, Chakrabarty, 2007;Gray, 2009]. Entropy is a measure of the scattering of possible states of a system as it changes (developed) over time.…”

Section: Input-oriented Modelmentioning

confidence: 99%

Company sustainable growth as the result of interaction between finance, energy, environmental and social factors (in case of JSC “Gazprom”)

Стеблянская

Ванг

Денисов

et al. 2020

SUJES

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values and degree of importance to obtain a common performance indicator (CRS), which can significantly improve the discrimination of sustainable growth models. To visualize the transformation of the stability of the system, it is advisable to use the negentropy index. The following factors influence the SGSI level: production, energy saving, environmental rating, environmental footprint, reduction of air pollutant emissions, reduction of wastewater discharges to surface water bodies, environmental expenditures, personnel costs, social expenses, financial leverage, self-financing ratio, and EBITDA.

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Boltzmann–shannon Entropy: Generalization and Application

Cited by 10 publications

References 6 publications

The Role of Entropy in the Development of Economics

The Role of Entropy in the Development of Economics

Using Weighted Entropy to Rank Chemicals in Quantitative High-Throughput Screening Experiments

Company sustainable growth as the result of interaction between finance, energy, environmental and social factors (in case of JSC “Gazprom”)

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