We study the connected components of the stochastic geometry model on
Poisson points which is obtained by connecting points with a probability
that depends on their relative position. Equivalently, we investigate
the random clusters of the ran- dom connection model defined on the
points of a Poisson process in d-dimensional space where the links are
added with a particular probability function. We use the
functions of the cluster size distribution in the statistical mechanics
of extensive and non-extensive. By comparing these obtained functions
with the probability function predicted by Penrose, we provide a
suitable approximate probability function. More- over, we relate this
stochastic geometry model to the physics literature by showing how the
fluctuations of the thermodynamic quantities of this model correspond to
other models when a phase transition (10.1002/mma.6965, 2020) occurs.
Also, we obtain the critical point using a new analytical method.