محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | Recurso digital |
| اللغة: | |
| منشور في: |
Zenodo
2025
|
| الوصول للمادة أونلاين: | https://doi.org/10.5281/zenodo.14867959 |
| الوسوم: |
إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
|
جدول المحتويات:
- <p>In (1), it is stated that a Tsallis distribution may describe a physical situation in which there are temperature variations (or even fluctuations). For example, in a heavy ion collision, various regions with different temperatures may be created with each representing its own Maxwell-Boltzmann exp(-e/T) equilibrium. Given this physical scenario, (1) fits the known Tsallis distribution: { 1- (1-q)e/T) } power 1/(1-q) to Integral db F(b) exp(-eb) where b=1/T. Based on their work in (2) using Mellin transformations, (1) suggests that F(b) is the argument of a gamma function which it explicitly lists. In other words, the goal is to start with a priori knowledge of the Tsallis distribution and find an appropriate F(b) which happens mathematically to be a gamma function integrand.</p> <p> Here, we note that if instead of the Maxwell-Boltzmann weight, exp(-e/T), used in (1), a uniform distribution 1 is employed instead, one would have (using the result of (1)): Integral db f(b) = Gamma(z+1) = z!, where z+1 is the exponent in the gamma function argument. We suggest that the z! factorial might have statistical significance on its won. In particular, the value of z is linked with bobo/ (sigma*sigma) - 2 ((1)). Here bo is the average 1/To over the regions with various temperatures and sigma*sigma, the variance of b. Given that one deals with square values in calculating variance, bobo appears instead of 1/T. It seems that the z! interpretation of the gamma function may mean that ((1)) represents a number of “quanta” so to speak which may be arranged (permuted) z! ways in order to create a statsical weight. If there is some physical/statsical relevance to this assumption, we argue that it serves as an a priori approach to deriving the Tsallis distribution. In other words, one does not have to fit the known Tsallis distribution to a gamma function integrand multiplied by exp(-e/T), but may choose the gamma function integrand a priori based on the idea of z!, thus obtaining the Tsallis distribution when one introduces the Maxwell-Boltzmann factor exp(-eb).</p> <p> </p>