Superstatistical properties of the Dirac oscillator with gamma, lognormal, and F distributions

We explore the thermal characteristics of fermionic fields with a nonminimal coupling in one, two, and three dimensions using the framework of superstatistics theory. We consider three distinct distributions: the gamma distribution, the lognormal distribution, and the F distribution. Each of these distributions is governed by a specific probability density function. To calculate the partition function, we use the Euler–Maclaurin formula, specifically in the low-energy asymptotic approximation of superstatistics. This calculation takes the remainder term into consideration. In each scenario, using the derived partition functions, we analyze the variations in entropy and specific heat with varying temperatures and the universal parameter denoted as \(q\). In general, we observe that increasing the value of \(q\) enhances all the curves. Additionally, we note that entropy values tend to increase as the temperature decreases, and tend to decrease as the parameter \(q\) increases.