Inference of the Universal Constancy of Planck Constant based on First Principles

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.