scholarly journals Mesoscopic Description of the Adiabatic Piston: Kinetic Equations and $${\mathcal {H}}$$-Theorem

2019 ◽  
Vol 176 (5) ◽  
pp. 1138-1160 ◽  
Author(s):  
Nagi Khalil
1993 ◽  
Vol 03 (01) ◽  
pp. 119-129 ◽  
Author(s):  
Yu. L. KLIMONTOVICH

The method of reconstruction of Fokker-Planck and Master equations for nonlinear open systems on the basis of experimental time series is considered. In the process of time evolution the entropy of a system, renormalized to the given value of the mean effective energy, increases in accordance with the kinetic equations (H-theorem). The evolution of the renormalized entropy of stationary states in the space of rule (control) parameters is also considered (S-theorem).


1973 ◽  
Vol 10 (3) ◽  
pp. 425-431
Author(s):  
Ta-Ming Fang

A previously developed set of kinetic model equations for a chemically-reacting gas is modified. By examining closely the H theorem, a new set of constraints is obtained. These conditions are then used to determine the inelastic collision parameters proposed in the model. The kinetic equations so obtained are able to produce exactly the same rate equations as prescribed by the actual chemical reactions.


1992 ◽  
Vol 171 (1-2) ◽  
pp. 26-30 ◽  
Author(s):  
J. Camacho ◽  
D. Jou
Keyword(s):  

Physics ◽  
2019 ◽  
Vol 1 (2) ◽  
pp. 229-253
Author(s):  
Sergey Adzhiev ◽  
Janina Batishcheva ◽  
Igor Melikhov ◽  
Victor Vedenyapin

The question of constructing models for the evolution of clusters that differ in shape based on the Boltzmann’s H-theorem is investigated. The first, simplest kinetic equations are proposed and their properties are studied: the conditions for fulfilling the H-theorem (the conditions for detailed and semidetailed balance). These equations are to generalize the classical coagulation–fragmentation type equations for cases when not only mass but also particle shape is taken into account. To construct correct (physically grounded) kinetic models, the fulfillment of the condition of detailed balance is shown to be necessary to monitor, since it is proved that for accepted frequency functions, the condition of detailed balance is fulfilled and the H-theorem is valid. It is shown that for particular and very important cases, the H-theorem holds: the fulfillment of the Arrhenius law and the additivity of the activation energy for interacting particles are found to be essential. In addition, based on the connection of the principle of detailed balance with the Boltzmann equation for the probability of state, the expressions for the reaction rate coefficients are obtained.


2018 ◽  
Vol 64 (1) ◽  
pp. 37-59 ◽  
Author(s):  
Victor V Vedenyapin ◽  
Sergey Z Adzhiev ◽  
Vladlena V Kazantseva

In this paper, we prove the H-theorem for generalized chemical kinetics equations. We consider important physical examples of such a generalization: discrete models of quantum kinetic equations (Uehling-Uhlenbeck equations) and a quantum Markov process (quantum random walk). We prove that time averages coincide with Boltzmann extremals for all such equations and for the Liouville equation as well. This gives us an approach for choosing the action-angle variables in the Hamilton-Jacobi method in a non-Hamiltonian context. We propose a simple derivation of the Hamilton-Jacobi equation from the Liouville equations in the finite-dimensional case.


1996 ◽  
Vol 21 (5) ◽  
pp. 461-502 ◽  
Author(s):  
E. Suraud

1993 ◽  
Vol 28 (2) ◽  
pp. 135-144 ◽  
Author(s):  
S. Matsui ◽  
R. Ikemoto Yamamoto ◽  
Y. Tsuchiya ◽  
B. Inanc

Using a fluidized bed reactor, experiments on glucose decomposition with and without sulfate reduction were conducted. Glucose in the reactor was mainly decomposed into lactate and ethanol. Lactate was mainly decomposed into propionate and acetate, while ethanol was decomposed into propionate, acetate, and hydrogen. Sulfate reduction was not involved in the decomposition of glucose, lactate, and ethanol, but was related to propionate and acetate decomposition. The stepwise reactions were modeled using either a Monod expression or first order reaction kinetics in respect to the reactions. The coefficients of the kinetic equations were determined experimentally. The modified Monod and first order reaction equations were effective at predicting concentrations of glucose, lactate, ethanol, propionate, acetate, and sulfate along the beight of the reactor. With sulfate reduction, propionate was decomposed into acetate, while without sulfate reduction, accumulation of propionate was observed in the reactor. Sulfate reduction accelerated propionate conversion into acetate by decreasing the hydrogen concentration.


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