Overview of some results in my thermodynamics, quantum mechanics, and molecular dynamics simulations research

摘要

Described here in sectional form are some simultaneous developments and results in [A] Continuum thermodynamics with applications, including electrochemical systems, [B] Statistical thermodynamics [C] Foundational studies in mechanics, quantum mechanics and radiation, and [D] Molecular dynamics and NEMD simulations of complex systems which are chemical reaction theories deduced from computer simulations. These topics were investigated over a two decade period on a mainly individual basis. [A] describes the postulated entropy forms for steady states by extending the results of Benofy and Quay, and by viewing any single nonequilibrium system as an ensemble of different thermodynamical states, show that the Prigogine results of minimum entropy production to be only approximations even at the linear regime. By studying the nature of Fourier heat conduction and equating this form of energy as being exclusively that due to heat, reciprocity to any order was derived with no reference to time reversal arguments. A potential theory using trivial EulerLagrange variations was advanced and applied to transport processes. Using the basic axioms of thermodynamics, the very influential B.C. Eu theory of an excess entropy thermodynamical function of state was disproved. Again, from basic Kelvin Clausius Second law considerations, a new and analytically exact diathermal entropy form was deduced. Some minor results of M.A. Biot are contradicted and an ambiguity in standard multicomponent thermodynamics is also illustrated. [B] describes a zero entropy trajectory (not connected with the Liouville equation and its coordinate space) with applications provided. A simple theorem relating the work increment of a system with the velocity correlation function resembling the correlation function for the self-diffusion coefficient is described, and a Brownian motion treatment of a blackbody cavity resonator shows that the Planck constant can be related to the relaxation time of the electronic oscillators lining the cavity and other related variables. An ideal flat 1-D surface of charged oscillators is predicted according to this theory to have a predominantly linear Fourier-like thermal energy emission and not the assumed T 4 Stefan type. Other workers relating classical theory to the quantum are mentioned. The central equation of dynamics, the Liouville equation is analytically disproved and an alternative stochastic form derived. Various phenomena in electrochemistry is examined ab initio. The central electrochemical assumption of constancy of the electron chemical potential and the Stern model assumption are questioned through elementary computations and various electrode capacitance and potential theorems are developed, including another electrochemical potential of possible importance in solid state theory. A triple unit convention for experimental quantities is proposed. [C] describes extensions to the Kirchoff radiation law, and proves for a common domain space, the Heisenberg uncertainty principles cannot obtain from Schrodinger wavefunctions and operators with the common domain space.