Abstract
Entropy is a measure used to measure uncertainty and disorder. The entropy measure contributes to the solution of many problems. There are different definitions of entropy used. The α value used in different ways offers new perspectives, new solutions and methods. Being able to choose the appropriate α value brings it closer to the solution. In this study, the effect of α value, which is used in some entropy definitions, on entropy criteria was examined. It was tried to understand in which direction it behaved and its effect on the criterion. With different variations and different α values, it was shown in which direction the entropy values took. It has been determined how it behaves through the xlogx and logx functions. Entropic behaviors were shown with graphs.
Keywords
References
- Ben-Naim, A. (2008). A Farewell To Entropy : Statistical Thermodynamics Based On Information. World Scientific Publishing Co. Pte. Ltd.
- Boltzmann, L. (1964). Lectures on Gas Theory. University of California Press.
- Bridgman, P. W. (1950). The Thermodynamics of Plastic Deformation and Generalized Entropy. Reviews of Modern Physics, 22(1), 56–63. https://doi.org/10.1103/RevModPhys.22.56
- Coraddu, M., Lissia, M., & Tonelli, R. (2006). Statistical descriptions of nonlinear systems at the onset of chaos. Physica A: Statistical Mechanics and Its Applications, 365(1), 252–257. https://doi.org/10.1016/j.physa.2006.01.007
- Karci, A. (2016). Fractional order entropy: New perspectives. Optik, 127(20), 9172–9177. https://doi.org/10.1016/j.ijleo.2016.06.119
- Rényi, A. (1961). On measures of entropy and information. Fourth Berkeley Symposium on Mathematical Statistics and Probability, 547. https://doi.org/10.1021/jp106846b
- Savare, G., & Toscani, G. (2014). The Concavity of Rényi Entropy Power. IEEE Transactions on Information Theory, 60(5), 2687–2693. https://doi.org/10.1109/TIT.2014.2309341
- Tuğal, İ., & Karcı, A. (2019). Comparisons of Karcı and Shannon entropies and their effects on centrality of social networks. Physica A: Statistical Mechanics and Its Applications, 523, 352–363. https://doi.org/10.1016/j.physa.2019.02.026
- Uslu, S. (2009). Tsallis Entropy Inequality. Dokuz Eylül University. wikipedia.org. (Accessed:17.08.2022). Renyi entropy. https://en.wikipedia.org/wiki/Rényi_entropy
Abstract
Entropi belirsizliğin, düzensizliğin ölçülmesi için kullanılan bir ölçüttür. Entropi ölçüsü birçok problemin çözümüne katkı sunar. Entropinin kullanılan farklı tanımları vardır. Farklı şekillerde kullanılan α değeri yeni bakış açıları, yeni çözümler ve yöntemler sunar. Uygun α değerini seçebilmek çözüme yaklaştırır. Bu çalışmada bazı entropi tanımlarında kullanılan α değerinin entropi ölçütlerine etkisine bakıldı. Hangi yönde davranış gösterdiği, ölçüte etkisi anlaşılmaya çalışıldı. Farklı varyasyonlarla ve farklı α değerleri ile entropi değerlerinin ne yönde değerler aldığı gösterildi. xlogx ve logx fonksiyonları üzerinden ne yönde davranış gösterdiği tespit edildi. Entropik davranışlar grafiklerle gösterildi.
Keywords
References
- Ben-Naim, A. (2008). A Farewell To Entropy : Statistical Thermodynamics Based On Information. World Scientific Publishing Co. Pte. Ltd.
- Boltzmann, L. (1964). Lectures on Gas Theory. University of California Press.
- Bridgman, P. W. (1950). The Thermodynamics of Plastic Deformation and Generalized Entropy. Reviews of Modern Physics, 22(1), 56–63. https://doi.org/10.1103/RevModPhys.22.56
- Coraddu, M., Lissia, M., & Tonelli, R. (2006). Statistical descriptions of nonlinear systems at the onset of chaos. Physica A: Statistical Mechanics and Its Applications, 365(1), 252–257. https://doi.org/10.1016/j.physa.2006.01.007
- Karci, A. (2016). Fractional order entropy: New perspectives. Optik, 127(20), 9172–9177. https://doi.org/10.1016/j.ijleo.2016.06.119
- Rényi, A. (1961). On measures of entropy and information. Fourth Berkeley Symposium on Mathematical Statistics and Probability, 547. https://doi.org/10.1021/jp106846b
- Savare, G., & Toscani, G. (2014). The Concavity of Rényi Entropy Power. IEEE Transactions on Information Theory, 60(5), 2687–2693. https://doi.org/10.1109/TIT.2014.2309341
- Tuğal, İ., & Karcı, A. (2019). Comparisons of Karcı and Shannon entropies and their effects on centrality of social networks. Physica A: Statistical Mechanics and Its Applications, 523, 352–363. https://doi.org/10.1016/j.physa.2019.02.026
- Uslu, S. (2009). Tsallis Entropy Inequality. Dokuz Eylül University. wikipedia.org. (Accessed:17.08.2022). Renyi entropy. https://en.wikipedia.org/wiki/Rényi_entropy
Details
| Primary Language | English |
|---|---|
| Subjects | Computer Software, Software Testing, Verification and Validation |
| Journal Section | PAPERS |
| Authors | |
| Publication Date | December 7, 2022 |
| Submission Date | October 31, 2022 |
| Acceptance Date | November 15, 2022 |
| Published in Issue | Year 2022 Volume: Vol:7 Issue: Issue:2 |
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