The main objectives of this paper are five-fold. The first is to introduce a general
dynamic law for all physical motion systems, based on a new variational principle
with constraint-infinitesimals. The second is to postulate the potential-descending
principle (PDP). We show that PDP is a more fundamental principle than the first
and second laws in thermodynamics, and gives rise to dynamical equations for non-equilibrium
systems. The third is to demonstrate that the PDP is the first principle to
describe irreversibility of all thermodynamic systems, with thermodynamic potential
as the basic physical quantity, rather than entropy. The fourth objective is to examine
the problems faced by the Boltzmann equation. We show that the Boltzmann is not a
physical law, is created as a mathematical model to obey the entropy-increasing principle
(for dilute gases), and consequently is unable to faithfully describe Nature. The
fifth objective is to prove an orthogonal-decomposition theorem and a theorem on variation
with constraint-infinitesimals, providing the needed mathematical foundations
of the dynamical law of physical motion.