Detailed balancing, principle

Thus this operator must satisfy the necessary demands of the particle conservation law and detailed balance principle as was the case for its simpler analogue in Eq. (4.23) and Eq. (4.24). They are... 

Being applied for the relaxation of populations (k = 0), this equality expresses the demands of the detailed balance principle. This is simply a generalization of Eq. (4.25), which establishes the well-known relation between rates of excitation and deactivation for the rotational spectrum. It is much more important that equality (5.21) holds not only for k = 0 but also for k = 1 when it deals with relaxation of angular momentum J and the elements should not be attributed any obvious physical sense. The non-triviality of this generalization is emphasized by the fact that it is impossible to extend it to the elements of the four-index... 

Here a and b are considered as fitting parameters depending on temperature. De-excitation rate constants (s < 0) are obtained from the detailed balance principle. AH fitting laws differ in the pre-exponential factor in Eq. (5.70). In the PEG model... 

Debye phenomenon and theory 59-60, 198 dense media see orientational relaxation in dense media orientational diffusion 70 Debye plateau 6, 73, 81 dephasing see adiabatic dephasing detailed balance principle, spectral collapse 137... 

If the probability for the system to jump to the upper PES is small, the reaction is an adiabatic one. The advantage of the adiabatic approach consists in the fact that its application does not lead to difficulties of fundamental character, e.g., to those related to the detailed balance principle. The activation factor is determined here by the energy (or, to be more precise, by the free energy) corresponding to the top of the potential barrier, and the transmission coefficient, k, characterizing the probability of the rearrangement of the electron state is determined by the minimum separation AE of the lower and upper PES. The quantity AE is the same for the forward and reverse transitions. 

Equation (47) shows that in the Condon approximation the probabilities of forward and reverse transitions satisfy the detailed balance principle since the point q corresponds to the intersection of the potential energy surfaces (and free energy surfaces) where Haa = Hbb. Therefore, at the point q we have... 

Detailed Balancing, Principle of Chemical Reaction Chemical Kinetics... 

The adsorption rate constant kaAs is calculated using kAes given by Eq. (28) and the detailed balancing principle. 

This is because the dissociation products diffusing in the liquid cage can come in contact again and again, restoring the exciplex so that the rate of their final separation is given by Eq. (3.83). The ratio of k to k as well as kf to Wb fits the detailed balance principle for the reversible reaction (3.81) ... 

The rates of the forward and backward transfers with the free-energy excess AG relate to each other according to the detailed balance principle ... 

At thermodynamic equilibrium, Ttj must vanish for every reaction otherwise, the equilibrium could be shifted by adding catalysts or inhibitors to alter the nonzero rates TZj. Formal proofs of this "detailed balance principle are presented by de Groot and Mazur (1962). Therefore, setting 7 = 0 at equilibrium and using Eq. (2.4-3), we get... 

Since the detailed balance principle implies that in equilibrium the electron population of the dot has to be at a steady-state, // - lT = 0, we immediately arrive at the relation... 

In the assumption of the diffusivity controlled kinetics regime and applicability of detailed balanced principle the Eq. (1) transforms to the Eq. (2) ... 

Suppose now we are at equilibrium, when association and dissociation compensate each other. We may then apply the detailed balancing principle and say that the dissociation process must be a bimolecular reaction of the second order.4 From a knowledge of the equilibrium constant and of the experimental association rate, we may then infer the pseudoexperimental dissociation rate at equilibrium. It is rather fortunate that the association process does not require an activation energy, since in this case, its rate is the same out of equilibrium, where the experiments have been carried out, as it is at equilibrium, where the values are interesting. We then understand that the dissociation reactions of a diatomic molecule by a bimolecular process offer the two interesting possibilities ... 

Here E12 is the identity matrix of order 12, A is the transition rate matrix defined in Table IV of [84], and the coefficient g < 1 accounts for the decreased mobility of the chain in the slow medium, relative to the fast medium, rsio refers to the rate of transition of the environment from the slow to the fast state. The reverse transition rate rfag, is fixed by the detailed balance principle as... 

Using the detailed balance principle (8)-(9), one can obtain the ratios of forward and backward reaction rate coefficients ... 

Equation [7] expresses the balance between the flux of all other states X toward X (the second term on the right-hand side of eqn [7]), leading to an inaease of P(X, t), and the flux out of the StateX (the first term on the right-hand side of eqn [7]), leading to a decrease of P(X, t). Now, for the application of the importance sampling MC method in statistical physics, one requires that the transition probability W(X X ) satisfy the detailed balance principle with the (canonic) equilibrium distribution Peq(X) = Z" exp(-V(X)/feB r), Z being the partition ftinaion... 

Using 7-invariance and rotation-invariance conditions, one can obtain the detailed balance principle (DBF) which connects the differential cross sections for direct and inverse reactions (see e.g., refs. [1,2]),... 

Our purpose is not to deal with the above accurate correlation functions. However, we want to obtain approximate quantum time correlation functions from the classical fluctuation functions, which should satisfy the detailed balance principle. Defining ... 

---