相关论文: The Heats of Reactions. Calorimetry and Van't-Hoff…
In some cases, it is possible to show the conservation of energy by using equations of motion in mechanics. By considering these results, some people can think that the conservation of energy is the result of equations of motion or Newton's…
The first law of thermodynamics restates the law of conservation of energy. It partitions the change in energy of a system into two pieces, heat and work. While there is no ambiguity to define heat and work in classical thermodynamics,…
The collective phenomena in physics and cooperative phenomena in biology/chemistry is compared in terms of the variational description. The maximum energy dissipation principle is employed and the cost-like functional is chosen according to…
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…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…
Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action…
Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double''…
In a recent paper, PNAS, 118, e1921529118 (2021), it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature…
From an analysis of various types of data obtained in relativistic nuclear collisions, the following picture has emerged in thermal and hydrodynamical descriptions: as the fluid expands and cools, particles first undergo a chemical freeze…
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…
A complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It is shown that all the known results for reaction-diffusion equations with power…
We consider a generalisation of thermodynamics that deals with multiple conserved quantities at the level of individual quantum systems. Each conserved quantity, which, importantly, need not commute with the rest, can be extracted and…
This work presents a formalism to derive field quantities and conservation laws from the atomistic using the theory of distributions as the mathematical tool. By defining temperature as a derived quantity as that in molecular kinetic theory…
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…
According to the shock jump conditions, the total fluid's mass, momentum, and energy should be conserved in the entire simulation box. We perform the dynamical Monte Carlo simulations with the multiple scattering law for energy analysis.…
The one-dimensional viscous conservation law is considered on the whole line $$ u_t + f(u)_x=\eps u_{xx},\quad (x,t)\in\RR\times\overline{\RP},\quad \eps>0, $$ subject to positive measure initial data. The flux $f\in C^1(\RR)$ is assumed to…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
We analyze a category of problems that is of interest in many physical situations, including those encountered in introductory physics classes: systems with two well-delineated parts that exchange energy, eventually reaching a shared…
The problem of self forces and radiation reaction is solved by conservation of energy methods. The longstanding problem of constant acceleration is solved, and it is shown that the self force does indeed affect the particle's motion, as…
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…