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This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with $N$ species, $M$ reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs' macroscopic chemical…
We propose a conservation-dissipation formalism (CDF) for coarse-grained descriptions of irreversible processes. This formalism is based on a stability criterion for non-equilibrium thermodynamics. The criterion ensures that non-equilibrium…
The law of mass action is used widely. The law of mass action does not automatically conserve current, as is clear from mathematics of a simple case, chosen to illustrate the issues. The law of mass action does not force a series of…
Photothermal reactions, involving both photochemical and thermal reaction-steps, are the most abundant sequences in photochemistry. The derivation of their rate-laws is standardized, but the integration of these rate-laws has not yet been…
Two different methods have been employed to determine the plasma temperature in a laser-cluster fusion experiment on the Texas Petawatt laser. In the first, the temperature was derived from time-of-flight data of deuterium ions ejected from…
We study the behavior of the solution of a generalized damped KdV equation $u_t + u_x + u_{xxx} + u^p u_x + \mathscr{L}_{\gamma}(u)= 0$. We first state results on the local well-posedness. Then when $p \geq 4$, conditions on…
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation…
Recently, we have shown that thermal effects play a crucial role in speeding up the rate of bond-dissociation reactions. This was done by applying a simple temperature-shifted Arrhenius Law to the experimental data, corroborated with…
For each substance-like quantity, a theorem about its conservation or non-conservation can be formulated. For the electric charge e.g. it reads: Electric charge can neither be created nor destroyed. Such a statement is short and easy to…
We have numerically studied heat conduction in a few one-dimensional momentum-conserving lattices with asymmetric interparticle interactions by the nonequilibrium heat bath method, the equilibrium Green-Kubo method, and the heat current…
This work presents a reaction mechanism for oxygen plasmas, i.e. a set of reactions and corresponding rate coefficients that are validated against benchmark experiments. The kinetic scheme is validated in a DC glow discharge for gas…
The article sets forth comprehensive basics of thermodynamics of chemical equilibrium as balance of the thermodynamic forces. Based on the linear equations of irreversible thermodynamics, De Donder definition of the thermodynamic force, and…
We deduce from energy conservation a lower bound on the mass of any system capable of imparting a constant acceleration to a charged body. We also point out a connection between this bound and the so called dominant energy condition of…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
We study a micro and macroscopic model for chemical reactions with feedback between reactions and temperature of the solute. The first result concerns the quasipotential as the large-deviation rate of the microscopic invariant measure. The…
We study the mass dependence of various quantities (like the average and maximum density, collision rate, participant-spectator matter, temperature as well as time zones for higher density) by simulating the reactions at the energy of…
First, Second and Combined Laws of Thermodynamics are revised in terms of entropy change, partial entropy, partial volume, and chemical potential.
Symmetry properties of conservation laws of partial differential equations are developed by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law…
Making sense of complex inhomogeneous systems composed of many interacting species is a grand challenge that pervades basically all natural sciences. Phase separation and pattern formation in reaction-diffusion systems have been largely…
The straightforward application of energy and linear momentum conservation to the absorption/emission of photons by atoms allows to establish the essential features of laser cooling of two levels atoms at low laser intensities. The lowest…