Dynamic Law of Physical Motion and Potential-Descending Principle (Journal of Mathematical Study, 2017)
The main objectives of this paper are five-fold. The first is to introduce a generaldynamic law for all physical motion systems, based on a new variational principlewith constraint-infinitesimals. The second is to postulate the potential-descendingprinciple (PDP). We show that PDP is a more fundamental principle than the firstand second laws in thermodynamics, and gives rise to dynamical equations for non-equilibriumsystems. The third is to demonstrate that the PDP is the first principle todescribe irreversibility of all thermodynamic systems, with thermodynamic potentialas the basic physical quantity, rather than entropy. The fourth objective is to examinethe problems faced by the Boltzmann equation. We show that the Boltzmann is not aphysical law, is created as a mathematical model to obey the entropy-increasing principle(for dilute gases), and consequently is unable to faithfully describe Nature. Thefifth objective is to prove an orthogonal-decomposition theorem and a theorem on variationwith constraint-infinitesimals, providing the needed mathematical foundationsof the dynamical law of physical motion.