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 Euler–Lagrange 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. An initial postulate of “trivial” Euler–Lagrange variations which might conceivably be connected to null geodesics is mentioned, and basic ideas in quantum theory connected to EPR, ensembles, and de Broglie waves and group velocities are examined. The central understanding of “time reversibility” as used in the physical sciences is proven to be false and is contrasted to other more legitimate definitions. Initial experiments to test the Fourier-like thermal radiation are described, and new relations for the radiancy and Kirchoff laws are postulated. Section [D] presents results and theories derived from MD and NEMD simulations, in particular in thermodynamical systems with an elementary reaction. A new work–heat energy interconversion theorem is postulated and applied to several phenomena, including a rationalization of the Hammet–Taft–Curtin free energy relations and the determination of the free energy, entropy, and enthalpy of activation from the shape profile of the molecule along its transition state reaction pathway. A broad area has been covered and the future goals include consolidating the outlines of the theoretical results by corroborating experimental results and by also looking to other formulations to realize possible common ground.
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Dec 16, 2023
Fuad Nasir 
Open Access
