  Since its discovery by Max Planck in 1900, the Planck constant $h$ has been
demonstrated to be an universal constant, and its numerical value has been
accurately determined based on experiments. Up to the present however the
physical origin of this fundamental constant has not been well understood, and
the numerical value of it has not been {\it ab initio} predicted. $h$ is
characteristic in two respects: 1) it is a universal constant with respect to
all (quasi-) stationary dynamical processes of all matter particles and
radiation fields, and 2) it has a specific numerical value. A theoretical
inference of $h$, and a corresponding accounting for the physical origin of
$h$, therefore needs be achieved in both respects. This paper presents a
theoretical exploration in the first respect, a mathematical inference of the
universal constancy of $h$, based on the second law of thermodynamics, the
principle of least action and the probability theory.
