  The Froggatt-Nielsen mechanism and the multi-local field theory are
interesting and promising candidates for solving the naturalness problem in the
universe. These theories are based on the different physical principles: The
former assumes the micro-canonical partition function $\int {\cal{D}}\phi\
\prod_i \delta (S_i^{}-I_i^{})$, and the latter assumes the partition function
$\int {\cal{D}}\phi\ \exp\left(iS_M^{}\right)$ where $S_M^{}$ is the
multi-local action $\sum_i c_i^{}S_i^{}+\sum_{i,j}c_{i,j}^{}S_i^{}S_j^{}+\cdots
$. Our main purpose is to show that they are equivalent in the sense that they
predict the same fine-tuning mechanism. In order to clarify our argument, we
first study (review) the similarity between the Froggatt-Nielsen mechanism and
statistical mechanics in detail, and show that the dynamical fine-tuning in the
former picture can be understood completely in the same way as the
determination of the temperature in the latter picture. Afterward, we discuss
the multi-local theory and the equivalence between it and the the
Froggatt-Nielsen mechanism. Because the multi-local field theory can be
obtained from physics at the Planck/String scale, this equivalence indicates
that the micro-canonical picture can also originate in such physics. As a
concrete example, we also review the IIB matrix model as an origin of the
multi-local theory.
