Scaling Relations of Lognormal Type Growth Process with an Extremal Principle of Entropy

Wu, Zhanjun; Li, Juan; Bai, Chen-Yuan

doi:10.3390/e19020056

Cited by 7 publications

(4 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As it is not currently known what sets this quantity, here we explore two options: the first uses maximization of entropy production to set σ M " 1{ ? 6, which is fairly widely observed in natural processes [64]. This estimate should occur for large systems, but for small systems one would expect the variance to be set by shot noise instead, σ " a M iso {M inner , making use of the isolation mass defined in the next section.…”

Section: Choicesmentioning

confidence: 96%

Multiverse Predictions for Habitability: Number of Potentially Habitable Planets

Sandora

2019

Universe

View full text Add to dashboard Cite

How good is our universe at making habitable planets? The answer to this depends on which factors are important for life: Does a planet need to be Earth mass? Does it need to be inside the temperate zone? are systems with hot Jupiters habitable? Here, we adopt different stances on the importance of each of these criteria to determine their effects on the probabilities of measuring the observed values of several physical constants. We find that the presence of planets is a generic feature throughout the multiverse, and for the most part conditioning on their particular properties does not alter our conclusions much. We find conflict with multiverse expectations if planetary size is important and it is found to be uncorrelated with stellar mass, or the mass distribution is too steep. The existence of a temperate circumstellar zone places tight lower bounds on the fine structure constant and electron to proton mass ratio.

show abstract

Section: Choicesmentioning

confidence: 96%

Multiverse Predictions for Habitability: Number of Potentially Habitable Planets

Sandora

2019

Universe

View full text Add to dashboard Cite

show abstract

“…Claude Shannon derived for the log-normal distribution the SHANNON SHAPE PARAMETER σ = 1/√6 ≈ 0.4082 based on the extremal principle of entropy. There are a lot of situations where this Shannon shape parameter determines very well the observed experimental data, e.g., [37] where is a very good introduction to this Shannon model. We assume that the Solar gravitational field interplays with all Maxwell-Boltzmann particles and the combination of microscopic redshifted speeds of individual particles results in a single macroscopic redshift speed determined by the Einstein median.…”

Section: The Es Log-normal Distributionmentioning

confidence: 99%

The ES Log-normal Distribution Determined by the Einstein Median as the Scale Parameter and the Shannon Shape Parameter

Stávek¹

2022

EJPHYSICS

View full text Add to dashboard Cite

The guiding principle of this contribution is the mutual interplay between the Solar gravitational field and the Maxwell-Boltzmann distribution of speeds of atoms and the observed Fraunhofer lines. We know from numerous experiments that the Newtonian gravitational constant does not depend on the atomic mass, temperature, pressure and many other particle parameters. Therefore, we should discover a universal distribution function that could be used for all atoms and their properties for a given gravitational field. We have introduced the ES log-normal distribution fully determined by the Einstein median as the scale parameter and the Shannon shape parameter σ = 1/√6. Shannon formulated this shape parameter for the log-normal distribution describing systems with the maximum entropy formation. This ES log-normal distribution function determines the most effective mutual interactions between the gravitational field and the Maxwell-Boltzmann particles. In order to make the Einstein median formula more general, we have introduced the model of the active solid angle of the source of gravity with values 1 ≤ Ω ≤ 4 steradians. We have tested this ES log-normal distribution with three datasets measured on the Solar disc and two datasets measured on the surface of the Earth using the Mössbauer effect. There were predicted some new properties of those datasets. This model might stimulate and promote new initiatives to collect new better datasets for the Solar disc and the Mössbauer effect.

show abstract

“…There are a lot of situations where this Shannon shape parameter determines very well the observed experimental data, e.g. [30] with a very good introduction to this Shannon model.…”

Section: The Es Log-normal Distribution Of Gravitational Phonon Veloc...mentioning

confidence: 99%

How to Interpret Gravitational Events in the Newton´s Rotating Bucket? (Gravitational Phonons)

Stávek¹

2022

EJPHYSICS

View full text Add to dashboard Cite

The Newton´s rotating bucket with gravitational events occurring in that bucket is a starting point for any new model describing gravitational situations and serves as a “filter” for any proposed gravitational model. The topic of this contribution is to describe the self-organization of H2O molecules in the rotating bucket based on the Einstein-Shannon (ES) log-normal distribution of gravitationally redshifted velocities of H2O molecules. The joint co-operation of the Earth´s gravitational field with the centrifugal force acts as that “hidden” organizing agent. H2O molecules transfer the gravitational phonons and reflect them on the surfaces of the wall, bottom, and the water surface of Newton´s bucket and form the 3D paraboloid. Five new experimental predictions are proposed and compared with the experiments. The external observer is unaware that the H2O molecules in Newton´s bucket are phonon velocity-organized due to the Earth´s gravitational redshift and the rotation of Newton´s bucket. The microscopic interplay of gravitational phonons inside of Newton´s bucket is hidden from the macroscopic analysis of the external observers. The external observer claims that these centrifugal forces are fictitious. In order to discover the real actions of those self-organized forces, the observer has to be a part of the rotating system in the presence of the Earth´s gravitational field or to study the rotating system in proposed experiments.

show abstract

Scaling Relations of Lognormal Type Growth Process with an Extremal Principle of Entropy

Cited by 7 publications

References 26 publications

Multiverse Predictions for Habitability: Number of Potentially Habitable Planets

Multiverse Predictions for Habitability: Number of Potentially Habitable Planets

The ES Log-normal Distribution Determined by the Einstein Median as the Scale Parameter and the Shannon Shape Parameter

How to Interpret Gravitational Events in the Newton´s Rotating Bucket? (Gravitational Phonons)

Contact Info

Product

Resources

About