  A general statistical thermodynamic theory that considers given sequences of
x-integers to play the role of particles of known type in an isolated elastic
system is proposed. By also considering some explicit discrete probability
distributions p_{x} for natural numbers, we claim that they lead to a better
understanding of probabilistic laws associated with number theory. Sequences of
numbers are treated as the size measure of finite sets. By considering p_{x} to
describe complex phenomena, the theory leads to derive a distinct analogous
force f_{x} on number sets proportional to $(\frac{\partial p_{x}}{\partial x}
)_{T}$ at an analogous system temperature T. In particular, this yields to an
understanding of the uneven distribution of integers of random sets in terms of
analogous scale invariance and a screened inverse square force acting on the
significant digits. The theory also allows to establish recursion relations to
predict sequences of Fibonacci numbers and to give an answer to the interesting
theoretical question of the appearance of the Benford's law in Fibonacci
numbers. A possible relevance to prime numbers is also analyzed.
