Volume 50, Issue 3
Dynamic Law of Physical Motion and Potential-Descending Principle

Tian Ma & Shouhong Wang

J. Math. Study, 50 (2017), pp. 215-241.

Published online: 2017-09

[An open-access article; the PDF is free to any online user.]

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  • Abstract

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.

  • AMS Subject Headings

82B05, 82B10, 82C10, 82C40, 35Q20, 35Q82

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

matian56@sina.com (Tian Ma)

showang@indiana.edu (Shouhong Wang)

  • BibTex
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@Article{JMS-50-215, author = {Ma , Tian and Wang , Shouhong}, title = {Dynamic Law of Physical Motion and Potential-Descending Principle}, journal = {Journal of Mathematical Study}, year = {2017}, volume = {50}, number = {3}, pages = {215--241}, abstract = {

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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v50n3.17.02}, url = {http://global-sci.org/intro/article_detail/jms/10618.html} }
TY - JOUR T1 - Dynamic Law of Physical Motion and Potential-Descending Principle AU - Ma , Tian AU - Wang , Shouhong JO - Journal of Mathematical Study VL - 3 SP - 215 EP - 241 PY - 2017 DA - 2017/09 SN - 50 DO - http://doi.org/10.4208/jms.v50n3.17.02 UR - https://global-sci.org/intro/article_detail/jms/10618.html KW - Dynamical law of physical motion, potential-descending principle, statistical physics, thermodynamics, entropy, irreversible processes, Boltzmann equation, orthogonal-decomposition theorem, variation with constraint-infinitesimals. AB -

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.

Tian Ma & Shouhong Wang. (2019). Dynamic Law of Physical Motion and Potential-Descending Principle. Journal of Mathematical Study. 50 (3). 215-241. doi:10.4208/jms.v50n3.17.02
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