preprints.org > physical sciences > mathematical physics > doi: 10.20944/preprints202408.1039.v1 (registering DOI)

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 14 August 2024 / Approved: 14 August 2024 / Online: 14 August 2024 (15:15:39 CEST)

In this paper, we introduce generalized entropy, the acceleration of its entropy and its the partial entropy. We assume that generalized entropy can be expressed as a second-order polynomial by applying the idea of logistics function to its entropy. In other words, we assume that the acceleration of generalized entropy is a constant. Besides, we show that the inverse of the partial entropy can express Newton's classical gravity, which is an inverse square law. By applying these concepts, we attempt to explain that 1) Gravity is constant within small distances with some conditions, It is possible that there exists 6-states within the distance R is small. Furthermore, within small distance, we show the possibility that the gravitational potential and the Coulomb potential can be treated in the same way. that 2) The rotation speed of a galaxy does not depend on its radius if the radius is within the size level of the universe. (the galactic rotation curve problem), and that 3) The gravitational acceleration toward the center changes at long distances compared to the classical theory of gravity. Furthermore, we show that the possibility of the existence of some constants which controls gravity and the speed of galaxies, and that gravity may relate on entropy.

Entropy, Gravity, Galaxy rotation curve, MOND, Planck's law, Dynamical system, Inverse square law, Logistic function

Physical Sciences, Mathematical Physics

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