Entropy and Its Application to Number Theory

Seiji Fujino

doi:10.20944/preprints202203.0371.v1

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preprints.org > physical sciences > thermodynamics > doi: 10.20944/preprints202203.0371.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Entropy and Its Application to Number Theory

Seiji Fujino

Version 1 : Received: 27 March 2022 / Approved: 29 March 2022 / Online: 29 March 2022 (03:02:06 CEST)
Version 2 : Received: 6 June 2022 / Approved: 7 June 2022 / Online: 7 June 2022 (04:14:37 CEST)
Version 3 : Received: 16 November 2023 / Approved: 16 November 2023 / Online: 17 November 2023 (08:59:25 CET)
Version 4 : Received: 28 November 2023 / Approved: 29 November 2023 / Online: 29 November 2023 (10:59:25 CET)
Version 5 : Received: 18 December 2023 / Approved: 18 December 2023 / Online: 18 December 2023 (10:28:51 CET)
Version 6 : Received: 30 December 2023 / Approved: 30 December 2023 / Online: 30 December 2023 (16:24:49 CET)
Version 7 : Received: 8 January 2024 / Approved: 8 January 2024 / Online: 8 January 2024 (17:00:00 CET)

How to cite: Fujino, S. Entropy and Its Application to Number Theory. Preprints 2022, 2022030371. https://doi.org/10.20944/preprints202203.0371.v1 Fujino, S. Entropy and Its Application to Number Theory. Preprints 2022, 2022030371. https://doi.org/10.20944/preprints202203.0371.v1

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MDPI and ACS Style

Fujino, S. Entropy and Its Application to Number Theory. Preprints 2022, 2022030371. https://doi.org/10.20944/preprints202203.0371.v1

APA Style

Fujino, S. (2022). Entropy and Its Application to Number Theory. Preprints. https://doi.org/10.20944/preprints202203.0371.v1

Chicago/Turabian Style

Fujino, S. 2022 "Entropy and Its Application to Number Theory" Preprints. https://doi.org/10.20944/preprints202203.0371.v1

Abstract

In this paper, we propose the expansion of the Planck distribution functions which is derived from the Boltzmann principle. Furthermore, we examine to expand Planck's law using new distribution functions. Moreover, using the ideas applied to the expansion of the Planck distribution function, we show that the derivation of Von Koch's inequality without using the Riemann Hypothesis and the negative of the abc conjecture. Besides, we describe some issues for the future.

Keywords

Entropy; Boltzmann principle; Planck’s law; Dynamical system; Von Koch’s inequality; Riemann Hypothesis; abc conjecture

Subject

Physical Sciences, Thermodynamics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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